VMLC
Release-50
Tags:Riemann SumArea under a curveMidpointsHow-To Calculus

Estimating Area With a Midpoint Riemann Sum

Author: ShaNisaa RaSun
The following problem is solved in this video. It is recommended that you try to solve the problem before watching the video. You can click "Answer" to reveal the answer to the problem.

Exercises

88

Related Videos (130)

Estimating Area With a Left-Hand Riemann Sum

Estimating Area With a Left-Hand Riemann Sum thumbnail
Estimating the area under a curve using left-hand Riemann sums

Introduction to Riemann Sums

Introduction to Riemann Sums thumbnail
Estimating the area under a function using right-hand, left-hand, and midpoint Riemann sums

Estimating Area With a Right-Hand Riemann Sum

Estimating Area With a Right-Hand Riemann Sum thumbnail
Estimating the area under a curve using right-hand Riemann sums

Estimating the Area Under a Curve With a Riemann Sum

Estimating the Area Under a Curve With a Riemann Sum thumbnail
Estimating the area under a graph using right-hand Riemann sums

MLC WIR 20B M151 week8 #7c

MLC WIR 20B M151 week8 #7c thumbnail
Using Riemann sums to estimate the area under a curve using midpoints

Riemann Sums and Definite Integrals: MATH 151 5.2 Problems 6-12

Riemann Sums and Definite Integrals: MATH 151 5.2 Problems 6-12 thumbnail
Using Reimann sums and the Fundamental Theorem of Calculus

Riemann Sums and Definite Integrals: MATH 151 5.3 Problems 6-12

Riemann Sums and Definite Integrals: MATH 151 5.3 Problems 6-12 thumbnail
Using Riemann sums and the Fundamental Theorem of Calculus

Riemann Sums: MATH 151 5.1 Problems 1-5

Riemann Sums: MATH 151 5.1 Problems 1-5 thumbnail
Riemann sums, including approximating areas under curves.

Area Between Curves: MATH 172 Problems 1-3

Area Between Curves: MATH 172 Problems 1-3 thumbnail
Interpreting integrals to represent areas between curves

Area with Riemann Sums and the Definite Integral

Area with Riemann Sums and the Definite Integral thumbnail
The definition of the Riemann Sum and how it relates to a definite integral

Calculating a Definite Integral From a Graph

Calculating a Definite Integral From a Graph thumbnail
Calculating a definite integral by finding the area under a curve using geometry

Calculating the Exact Area Under a Curve With Geometry

Calculating the Exact Area Under a Curve With Geometry thumbnail
Using geometric formulas for circles, triangles, and rectangles to find the exact area under a curve

Definite Integrals: MATH 171 Problems 5-9

Definite Integrals: MATH 171 Problems 5-9 thumbnail
The definition and properties of definite integrals

Definite Integrals: MATH 172 Review

Definite Integrals: MATH 172 Review thumbnail
Review of the definition of a definite integral

Hydrostatic Force: MATH 172 Problems 6 & 7

Hydrostatic Force: MATH 172 Problems 6 & 7 thumbnail
Using Riemann Sums and Integrals to calculate hydrostatic force

MLC WIR 20B M151 week10 #20

MLC WIR 20B M151 week10 #20 thumbnail
Using Riemann sums with left endpoints to estimate the area under a curve

MLC WIR 20B M151 week8 #7a

MLC WIR 20B M151 week8 #7a thumbnail
Using Riemann sums to estimate the area under a curve using right endpoints

MLC WIR 20B M151 week8 #7b

MLC WIR 20B M151 week8 #7b thumbnail
Using Riemann sums to estimate the area under a curve using left endpoints

MLC WIR 20B M151 week8 #8

MLC WIR 20B M151 week8 #8 thumbnail
Using a limit of Riemann sums to write an expression for the area under a graph

MLC WIR 20B M151 week9 #11

MLC WIR 20B M151 week9 #11 thumbnail
Approximating the area under a curve using right endpoints

MLC WIR 20B M151 week9 #12

MLC WIR 20B M151 week9 #12 thumbnail
Approximating the area under a curve using left endpoints

MLC WIR 20B M151 week9 #13

MLC WIR 20B M151 week9 #13 thumbnail
Using a limit of Riemann sums to write an expression for the area under a graph

A Composition of Tangent and Arccosine

A Composition of Tangent and Arccosine thumbnail
Evaluating a composition of tangent and arccosine

Absolute Extrema on a Closed Interval

Absolute Extrema on a Closed Interval thumbnail
Finding the absolute maximum and minimum of a rational function on two closed intervals

Absolute Extrema on a Closed Interval 2

Absolute Extrema on a Closed Interval 2 thumbnail
Finding the absolute maximum and absolute minimum of a rational function on two closed intervals

Approximating Definite Integrals with Riemann Sums in Python

Approximating Definite Integrals with Riemann Sums in Python thumbnail
Using Python to approximate a definite integral using left endpoint Riemann sums

Arc Length of a Curve: MATH 172 Problems 3 & 4

Arc Length of a Curve: MATH 172 Problems 3 & 4 thumbnail
Deriving and using the formula for the arc length of a curve

Area Between Curves

Area Between Curves thumbnail
Using Riemann sums to find the definite integral for the area between curves

Area Between Two Curves

Area Between Two Curves thumbnail
Finding the area between two curves on an interval using a definite integral

Area of the Region Bounded by Two Curves

Area of the Region Bounded by Two Curves thumbnail
Finding the area of a region bounded by two curves using definite integrals

Average Rate of Change from a Table

Average Rate of Change from a Table thumbnail
Finding the average rate of change over time periods from a table

Average Value of a Function

Average Value of a Function thumbnail
Finding the average value of a a function on an interval using a definite integral

Average Value of a Function: MATH 172 Problems 6-8

Average Value of a Function: MATH 172 Problems 6-8 thumbnail
Calculating the average value of a function and proving the Mean Value Theorem for Integrals

Calculating Marginal Revenue

Calculating Marginal Revenue thumbnail
Finding the marginal revenue given the price-demand function for a word problem

Calculating Profit From Marginal Profit Using u-Substitution

Calculating Profit From Marginal Profit Using u-Substitution thumbnail
Calculating profit from marginal profit using an indefinite integral and u-substitution

Calculating the Rate of Growth With Compound Interest

Calculating the Rate of Growth With Compound Interest thumbnail
Finding the rate a balance is increasing for interest compounded monthly and continuously

Calculating Work Using Integrals: MATH 172 Problems 4 & 5

Calculating Work Using Integrals: MATH 172 Problems 4 & 5 thumbnail
Using integrals to calculate work done in physics examples

Combinations of Limits from Graphs

Combinations of Limits from Graphs thumbnail
Finding limits of combinations of functions using their graphs

Continuity of a Function with a Cube Root

Continuity of a Function with a Cube Root thumbnail
Finding where a function with a fraction and cube root is continuous

Continuity of a Function with a Square Root and Logarithm

Continuity of a Function with a Square Root and Logarithm thumbnail
Determining where a function with a fraction, square root, and logarithm is continuous

Continuity of a Piecewise Function

Continuity of a Piecewise Function thumbnail
Determining where a piecewise function is continuous algebraically

Cylindrical Shell Method: MATH 172 Problems 1-3

Cylindrical Shell Method: MATH 172 Problems 1-3 thumbnail
Using cylindrical shells to calculate the volume of a rotational solid

Definite Integral Comparison Properties

Definite Integral Comparison Properties thumbnail
Comparing two definite integrals with the same limits of integration

Deriving the Formula for Cylindrical Shells

Deriving the Formula for Cylindrical Shells thumbnail
Deriving the formula for the method of cylindrical shells

Determining Where the Derivative Exists From a Graph

Determining Where the Derivative Exists From a Graph thumbnail
Determining where the derivative of a function does not exist from a graph

Evaluating a Definite Integral

Evaluating a Definite Integral thumbnail
Using the Fundamental Theorem of Calculus to evaluate a definite integral

Evaluating a Definite Integral 2

Evaluating a Definite Integral 2 thumbnail
Using the Fundamental Theorem of Calculus to evaluate a definite integral

Evaluating a Definite Integral with u-Substitution

Evaluating a Definite Integral with u-Substitution thumbnail
Using the Fundamental Theorem of Calculus and \(u\)-substitution to evaluate a definite integral

Evaluating a Limit Numerically

Evaluating a Limit Numerically thumbnail
Finding the limit of a function numerically using a calculator

Evaluating Derivatives From a Given Table

Evaluating Derivatives From a Given Table thumbnail
Finding and evaluating derivatives using values given in a table

Evaluating Limits Algebraically

Evaluating Limits Algebraically thumbnail
Using the properties of limits to find several limits algebraically

Evaluating Limits from a Graph

Evaluating Limits from a Graph thumbnail
Finding limits from the graph of a piecewise function

Evaluating One-Sided Limits from a Graph

Evaluating One-Sided Limits from a Graph thumbnail
Finding one-sided limits from the graph of a piecewise function

Finding a Derivative by Simplifying a Rational

Finding a Derivative by Simplifying a Rational thumbnail
Finding the derivative of a rational function by simplifying and using the power rule

Finding a Derivative with Exponential Functions and Logarithms

Finding a Derivative with Exponential Functions and Logarithms thumbnail
Finding the derivative a function with a power, exponential, and logarithm

Finding a Function from its Derivative and One Value

Finding a Function from its Derivative and One Value thumbnail
Solving for a function given its derivate and one value

Finding an Antiderivative

Finding an Antiderivative thumbnail
Finding the antiderivative of a function

Finding an Indefinite Integral

Finding an Indefinite Integral thumbnail
Evaluating an indefinite integral with an exponential

Finding an Indefinite Integral with a Fraction

Finding an Indefinite Integral with a Fraction thumbnail
Solving an indefinite integral by first simplifying the fraction

Finding Critical Values

Finding Critical Values thumbnail
Finding the critical values for several functions

Finding the Box with the Largest Volume

Finding the Box with the Largest Volume thumbnail
Finding the dimensions of the box with the largest volume given the amount of material to make the box

Finding the Cost Function from Marginal Cost

Finding the Cost Function from Marginal Cost thumbnail
Solving the antiderivative of marginal cost to find the cost function and evaluating a particular cost

Finding the Derivative of a Polynomial Using the Limit Definition

Finding the Derivative of a Polynomial Using the Limit Definition thumbnail
Using the limit definition to find the derivative of a polynomial

Finding the Derivative of a Rational Function Using the Limit Definition

Finding the Derivative of a Rational Function Using the Limit Definition thumbnail
Using the limit definition to find the derivative of a rational function

Finding the Derivative of a Root Function Using the Limit Definition

Finding the Derivative of a Root Function Using the Limit Definition thumbnail
Using the limit definition to find the derivative of a square root function

Finding the Function from Its Derivative Using u-Substitution

Finding the Function from Its Derivative Using u-Substitution thumbnail
Using u-substitution in an indefinite integral to find a function from its derivative and a given vaue

Finding the Price to Maximize Profit

Finding the Price to Maximize Profit thumbnail
Finding the selling price of trucks to maximize profit given the cost and price-demand functions

Finding Where a Function is Increasing and Decreasing

Finding Where a Function is Increasing and Decreasing thumbnail
Determining the intervals where a function is increasing and decreasing

Horizontal Asymptote of a Fraction with Exponential Functions

Horizontal Asymptote of a Fraction with Exponential Functions thumbnail
Finding the horizontal asymptotes of a function that is a fraction with exponentials in the numerator and denominator

Increasing and Decreasing and Local Extrema

Increasing and Decreasing and Local Extrema thumbnail
Finding the intervals where a function is increasing/decreasing and the local extrema

Increasing and Decreasing and Local Extrema for a Revenue Function

Increasing and Decreasing and Local Extrema for a Revenue Function thumbnail
Finding intervals of increase/decrease and the local extema for revenue from a word problem

Inflection Points and Intervals of Concavity for an Exponential Function

Inflection Points and Intervals of Concavity for an Exponential Function thumbnail
Finding the intervals of concavity and inflection points for a function with exponentials

Inflection Points and Intervals of Concavity from a Graph

Inflection Points and Intervals of Concavity from a Graph thumbnail
Determining the intervals of concavity and inflection points from the graph of a function

Instantaneous Rate of Change of a Function

Instantaneous Rate of Change of a Function thumbnail
Finding the exact value of the instantaneous rate of change

Instantaneous Rate of Change of a Rational Function

Instantaneous Rate of Change of a Rational Function thumbnail
Finding the exact value of the instantaneous rate of change

Instantaneous Rate of Change of Profit

Instantaneous Rate of Change of Profit thumbnail
Finding the instantaneous rate of change of profit for a given price-demand function and cost function

Integral and Comparison Tests: MATH 172 Problems 4-7

Integral and Comparison Tests: MATH 172 Problems 4-7 thumbnail
Proving the Integral, Comparison, and Limit Comparison Tests

Integrating Along y-axis for Area Between Curves

Integrating Along y-axis for Area Between Curves thumbnail
Determining whether its easier to integrate along the \(x\) or \(y\)-axis to find the area between curves

Limit at Negative Infinity of a Rational Function

Limit at Negative Infinity of a Rational Function thumbnail
Solving a limit approaching negative infinity for a rational function

Limit of a Fraction with a Square Root

Limit of a Fraction with a Square Root thumbnail
Finding the limit algebraically of a function with a square root in the numerator of a fraction

Limit of a Piecewise Function

Limit of a Piecewise Function thumbnail
Finding one and two-sided limits for a piecewise function algebraically

Limit of a Rational Function

Limit of a Rational Function thumbnail
Finding the limit of a rational function algebraically

Limit of a Rational Function 2

Limit of a Rational Function 2 thumbnail
Finding the limit of a rational function algebraically

Limit with an Absolute Value

Limit with an Absolute Value thumbnail
Finding the limit algebraically of a function with an absolute value

Limit with Multiple Fractions

Limit with Multiple Fractions thumbnail
Finding the limit algebraically of a function with multiple fractions

Limits at Infinity of a Fraction with Exponential Functions

Limits at Infinity of a Fraction with Exponential Functions thumbnail
Solving the limits approaching infinity and negative infinity with exponential functions in the numerator and denominator

Limits at Infinity of a Rational Function

Limits at Infinity of a Rational Function thumbnail
Solving the limits approaching infinity and negative infinity of a rational function

Limits at Infinity of a Rational Function 2

Limits at Infinity of a Rational Function 2 thumbnail
Solving the limits approaching infinity and negative infinity of a rational function

Local and Absolute Extrema from a Graph

Local and Absolute Extrema from a Graph thumbnail
Finding all local and absolute extrema of a function from a graph

MATH 152: Area Exercise 1

MATH 152: Area Exercise 1 thumbnail
Finding the area of a region bounded by two curves

MATH 152: Area Exercise 2

MATH 152: Area Exercise 2 thumbnail
Finding the area of a region bounded by two curves

MATH 152: Area Exercise 3

MATH 152: Area Exercise 3 thumbnail
Finding the area of a region bounded by two curves

Maximizing a Product of Numbers

Maximizing a Product of Numbers thumbnail
Finding the maximum product of two numbers given their sum is 100

Minimizing the Cost of a Box

Minimizing the Cost of a Box thumbnail
Finding the minimum cost of a box given the volume and cost of materials

MLC WIR 20B M151 week10 #21

MLC WIR 20B M151 week10 #21 thumbnail
Evaluating a definite integral by interpreting it as an area and using geometry

MLC WIR 20B M151 week9 #14a

MLC WIR 20B M151 week9 #14a thumbnail
Evaluating a definite integral by using geometry to find the area under the curve

MLC WIR 20B M151 week9 #14b

MLC WIR 20B M151 week9 #14b thumbnail
Evaluating a definite integral by using geometry to find the area under the curve

Part 1 of the Fundamental Theorem of Calculus

Part 1 of the Fundamental Theorem of Calculus thumbnail
Using Part 1 of the Fundamental Theorem of Calculus to find the derivative of a function defined using an integral

Slope of a Secant Line

Slope of a Secant Line thumbnail
Finding the slope of a secant line to a given function

Slope of a Tangent Line

Slope of a Tangent Line thumbnail
Finding the equation of the tangent line to a function using the limit definition

Solving a Related Rates Word Problem About a Sliding Ladder

Solving a Related Rates Word Problem About a Sliding Ladder thumbnail
Finding how fast a ladder moves up a wall as the bottom is being pushed

Solving a Related Rates Word Problem About Liquid Filling a Sphere

Solving a Related Rates Word Problem About Liquid Filling a Sphere thumbnail
Finding the rate water is flowing into an expandable sphere given the rate a sphere is growing

Solving a Related Rates Word Problem About Profit

Solving a Related Rates Word Problem About Profit thumbnail
Finding the rate of change of profit given the rate of increase for sales

Solving a Word Problem With a Definite Integral

Solving a Word Problem With a Definite Integral thumbnail
Solving a word problem using a definite integral and the Fundamental Theorem of Calculus

Solving for a Constant so a Piecewise Function is Continuous

Solving for a Constant so a Piecewise Function is Continuous thumbnail
Solving for a constant to make a piecewise-defined function continuous for all real numbers

The Quotient Rule with an Exponential

The Quotient Rule with an Exponential thumbnail
Finding the derivative of a fraction with an exponential using the Quotient Rule

Trapezoid Rule: MATH 172 Problems 1 & 2

Trapezoid Rule: MATH 172 Problems 1 & 2 thumbnail
Covering the Trapezoid Rule for approximating the value of an integral

Using Both the Quotient and Product Rule

Using Both the Quotient and Product Rule thumbnail
Finding a derivative using both the Product and Quotient Rule

Using Implicit Differentiation to Find a Derivative

Using Implicit Differentiation to Find a Derivative thumbnail
Using implicit differentiation to find the derivative of a function

Using Implicit Differentiation to Find a Derivative 2

Using Implicit Differentiation to Find a Derivative 2 thumbnail
Using implicit differentiation to find the derivative of a function

Using Log Properties to Simplify Before Taking the Derivative

Using Log Properties to Simplify Before Taking the Derivative thumbnail
Using logarithm properties to simplify before using the Chain Rule to find a derivative

Using Log Properties to Simplify Before Taking the Derivative 2

Using Log Properties to Simplify Before Taking the Derivative 2 thumbnail
Using logarithm properties to simplify before using the Generalized Logarithm Rule to find a derivative

Using Logarithmic Differentiation to Find a Derivative

Using Logarithmic Differentiation to Find a Derivative thumbnail
Finding the derivative of a function that requires logarithmic differentiation

Using the Alternate Form of the Chain Rule

Using the Alternate Form of the Chain Rule thumbnail
Using the alternate form of the Chain Rule to find the derivative

Using the Chain Rule with a Table

Using the Chain Rule with a Table thumbnail
Using the chain rule to find derivates with some values given in a table

Using the Generalized Exponential Rule

Using the Generalized Exponential Rule thumbnail
Using the Generalized Exponential Rule to find the derivative of a function

Using the Generalized Power Rule

Using the Generalized Power Rule thumbnail
Finding the derivative of a function using the Generalized Power Rule

Using the Product and Quotient Rules with a Table

Using the Product and Quotient Rules with a Table thumbnail
Finding a derivative using the Product and Quotient Rule and values given in a table

Using the Product Rule with a Logarithm

Using the Product Rule with a Logarithm thumbnail
Finding a derivative of a function with a logarithm using the Product Rule

Using the Product Rule with an Exponential

Using the Product Rule with an Exponential thumbnail
Finding the derivative of a function with a square root and exponential using the Product Rule

Using the Quotient Rule Twice to Find the Second Derivative

Using the Quotient Rule Twice to Find the Second Derivative thumbnail
Using the quotient rule twice to find the second derivative of a rational function

u-Substitution With a Natural Logarithm

u-Substitution With a Natural Logarithm thumbnail
Solving an indefinite integral with a natural logarithm using u-substitution

u-Substitution With a Quotient and a Root

u-Substitution With a Quotient and a Root thumbnail
Solving an indefinite integral with a cube root in the denominator using u-substitution

u-Substitution With a Quotient and Exponentials

u-Substitution With a Quotient and Exponentials thumbnail
Solving an indefinite integral with exponentials in a quotient using u-substitution

u-Substitution With an Exponential Function

u-Substitution With an Exponential Function thumbnail
Solving an indefinite integral with an exponential function suing u-substitution

Vectors: MATH 171 Problems 3 & 4

Vectors: MATH 171 Problems 3 & 4 thumbnail
Using vectors to prove the midpoint formula and a fact about quadrilaterals

Vectors: MATH 171 Problems 5 & 6

Vectors: MATH 171 Problems 5 & 6 thumbnail
Using vectors to prove facts about equilateral triangles and a scalar multiplication property for the dot product

Vertical Asymptotes and Holes of a Rational Function

Vertical Asymptotes and Holes of a Rational Function thumbnail
Finding the holes and vertical asymptotes of a rational function

Volume of a Solid: MATH 172 Problems 4-6

Volume of a Solid: MATH 172 Problems 4-6 thumbnail
Using the disk and washer method to calculate the volume of rotational solids

Where the Graph of a Function is Not Continuous

Where the Graph of a Function is Not Continuous thumbnail
Determining where a piecewise function is continuous from its graph
Texas A&M University Web Accessibility Site Policies