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MATH 152: Work Exercise 6

Calculating the work done pumping water out of a tank that is an upright cylinder

MATH 152: Work Exercise 7

Calculating the work done pumping water out of a rectangular tank

MATH 152: Work Exercise 8

Calculating the work done pumping water out of a tank shaped like a trough

MATH 152: Work Exercise 9

Calculating the work done pumping water out of a tank shaped like a trough

MATH 152: Work Exercise 10

Calculating the work done pumping water out of a cone-shaped tank

WIR 20B M152 V20

Finding the work to pump water out of a tank

WIR 20B M152 V21

Finding the work to pump water out of a tank

Work Done Pumping Water Out of a Tank

Explaining how to use integration to calculate the work done pumping water out of a tank

Work Done Pumping Water Out of a Tank

Explaining how to use integration to calculate the work done pumping water out of a tank

Calculating Work in Python: Hooke’s Law

Using Python to calculate the amount of work done in moving a spring using Hooke's Law

Review for the Common Exam: MATH 152 Exam 1 Review Problems 11-14

Review of work and average value

WIR 20B M152 V19

Solving work and force problems for a spring

MATH 152: Work Exercise 3

Calculating the work done moving an object with a variable force

MATH 152: Work Exercise 4

Calculating a spring constant and the work done stretching a spring

MATH 152: Work Exercise 5

Solving for a spring constant and calculating work done stretching a spring

Work Done Stretching a Spring Using Hooke's Law

How to use Hooke's Law to calculate the work done in stretching a spring

MATH 152: Work Exercise 11

Calculating the work done pulling a rope to the top of a building

MATH 152: Work Exercise 12

Calculating the work done pulling a rope and weight to the top of a building

MATH 152: Work Exercise 13

Calculating the work done pulling part of a rope to the top of a building

Review for the Common Exam: MATH 152 Exam 1 Review Problems 11-14

Review of work and average value

Work Done Stretching a Spring Using Hooke's Law

How to use Hooke's Law to calculate the work done in stretching a spring

Calculating Work Using Integrals: MATH 172 Problems 4 & 5

Using integrals to calculate work done in physics examples

Work and Average Value: MATH 152 Problems 1-9

Using integrals to solve work problems and find the average value

Approximating Definite Integrals with Riemann Sums in Python

Using Python to approximate a definite integral using left endpoint Riemann sums

Definite and Indefinite Integrals in Python

Solving definite and indefinite integrals in Python

Volumes of Revolution in Python

Finding the volume of a solid of revolution in Python

Areas Between Curves in Python

Using Python to identify the region between curves and then evaluate the area of the region

Calculating a Definite Integral From a Graph

Calculating a definite integral by finding the area under a curve using geometry

Properties of Definite Integrals

Evaluating a definite integral given the values of two other definite integrals of the same function

Definite Integral Comparison Properties

Comparing two definite integrals with the same limits of integration

Evaluating a Definite Integral

Using the Fundamental Theorem of Calculus to evaluate a definite integral

Evaluating a Definite Integral 2

Using the Fundamental Theorem of Calculus to evaluate a definite integral

Evaluating a Definite Integral with u-Substitution

Using the Fundamental Theorem of Calculus and \(u\)-substitution to evaluate a definite integral

Part 1 of the Fundamental Theorem of Calculus

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

Solving a Word Problem With a Definite Integral

Solving a word problem using a definite integral and the Fundamental Theorem of Calculus

Average Value of a Function

Finding the average value of a a function on an interval using a definite integral

Area Between Two Curves

Finding the area between two curves on an interval using a definite integral

Area of the Region Bounded by Two Curves

Finding the area of a region bounded by two curves using definite integrals

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

Using Reimann sums and the Fundamental Theorem of Calculus

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

Using Riemann sums and the Fundamental Theorem of Calculus

Integration by Substitution: MATH 151 5.5 Problems 13 & 14

Examples of integration by substitution

MLC WIR 20B M151 week9 #13

Using a limit of Riemann sums to write an expression for the area under a graph

MLC WIR 20B M151 week9 #14a

Evaluating a definite integral by using geometry to find the area under the curve

MLC WIR 20B M151 week9 #14b

Evaluating a definite integral by using geometry to find the area under the curve

MLC WIR 20B M151 week10 #21

Evaluating a definite integral by interpreting it as an area and using geometry

MLC WIR 20B M151 week10 #22

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

MLC WIR 20B M151 week10 #24a

Evaluating a definite integral containing a polynomial

MLC WIR 20B M151 week10 #24b

Evaluating a definite integral by first simplifying the integrand

MLC WIR 20B M151 week10 #24c

Evaluating a definite integral with an exponential and sine function

MLC WIR 20B M151 week10 #24e

Using u-substitution to evaluate an indefinite integral

Review for the Common Exam: MATH 152 Exam 1 a Review Problems 1-4

Reviewing u-Substitution

Review for the Common Exam: MATH 152 Exam 1 b Review Problems 29-33

Review of trigonometric substitution

Review for the Common Exam: MATH 152 Exam 1 b Review Problems 34 & 35

Review of partial fractions

Review for the Common Exam: MATH 152 Exam 3 b Review Problems 4 & 5

Review of using tests to determine if a series is absolutely convergent, convergent, and divergent

Review for the Common Exam: MATH 152 Exam 3 c Review Problems 10-13

Review of power series properties and writing functions as power series

Review for the Common Exam: MATH 152 Exam 3 c Review Problems 13-18

Review of Taylor and Maclaurin Series and their properties

Review for the Common Exam: MATH 152 Exam 3 c Review Problems 4 & 5

Review of using tests to determine if a series is absolutely convergent, convergent, and divergent

WIR 20B M152 V88

Finding the length of a curve given by parametric equations

WIR 20B M152 V89

Find the integral representing the surface area of a rotated parametric curve

WIR 20B M152 V90

Finding the surface area of a rotated parametric curve

WIR 20B M152 V95

Finding the area of a region defined using polar coordinates

WIR 20B M152 V96

Finding the area of a region defined using polar coordinates

WIR 20B M152 V97

Finding the area of a region defined using polar coordinates

WIR 20B M152 V98

Finding the area of a region defined using polar coordinates

WIR 20B M152 V99

Finding the area of a region defined using polar coordinates

WIR 20B M152 V80

Evaluating a definite integral by rewriting the integrand as its Maclaurin series

WIR 20B M152 V7

Finding the area of a region enclosed by two curves

WIR 20B M152 V8

Finding the area of a region enclosed by two curves

WIR 20B M152 V9

Finding the area of a region enclosed by two curves

WIR 20B M152 V10

Finding the area of a region bounded by curves

Area with Riemann Sums and the Definite Integral

The definition of the Riemann Sum and how it relates to a definite integral

Area Between Curves

Using Riemann sums to find the definite integral for the area between curves

Integrating Along y-axis for Area Between Curves

Determining whether its easier to integrate along the \(x\) or \(y\)-axis to find the area between curves

Area Between Curves Using Multiple Integrals

Using multiple integrals to find the area between two curves

MATH 152: Area Exercise 1

Finding the area of a region bounded by two curves

MATH 152: Area Exercise 2

Finding the area of a region bounded by two curves

MATH 152: Area Exercise 3

Finding the area of a region bounded by two curves

MATH 152: Area Exercise 4

Finding an integral representing the area of a region bounded by two curves

MATH 152: Area Exercise 5

Finding the area of a region bounded by two curves

MATH 152: Volume Exercise 1

Using the disk method to find the volume of a rotational solid

MATH 152: Volume Exercise 3

Using the disk method to find the volume of a rotational solid

MATH 152: Volume Exercise 4a

Using the washer method to set up an integral for the volume of a rotational solid

MATH 152: Volume Exercise 4b

Using the washer method to set up an integral for the volume of a rotational solid

MATH 152: Volume Exercise 4cd

Using the washer method to set up an integral for the volume of a rotational solid

MATH 152: Volume Exercise 5

Finding the volume of a non-rotation solid

MATH 152: Volume Exercise 6

Finding the volume of a non-rotational solid

MATH 152: Volume Exercise 7

Finding the volume of a non-rotational solid

WIR 20B M152 V11

Finding the volume of a non-rotational solid

WIR 20B M152 V12

Finding the volume of a non-rotational solid

WIR 20B M152 V13

Finding the volume of a solid of revolution using the disk method

WIR 20B M152 V14

Finding the volume of a solid of revolution using the disk method

WIR 20B M152 V15

Finding the volume of a solid of revolution using the washer method

WIR 20B M152 V16

Finding the volume of a solid of revolution using the washer method

WIR 20B M152 V17

Finding the volume of a solid of revolution using cylindrical shells

WIR 20B M152 V18

Finding the volume of a solid of revolution using cylindrical shells

Deriving the Formula for Cylindrical Shells

Deriving the formula for the method of cylindrical shells

Cylindrical Shells when Revolving Around y-axis

Explaining how to use cylindrical shells when the region is rotated around the \(y\)-axis

MATH 152: Cylindrical Shells Exercise 1

Using cylindrical shells to find the volume of a region rotated around the \(y\)-axis

MATH 152: Cylindrical Shells Exercise 2

Using cylindrical shells to find the volume of a region rotated around the \(y\)-axis

MATH 152: Cylindrical Shells Exercise 7

Using disks and shells to find the volume of a rotational solid

Definition of Work

Explaining the definition of work for constant and non-constant forces

Work Done Pulling Up a Rope

How to calculate the work done in lifting up a rope possibly with a mass

MATH 152: Work Exercise 1

Calculating the work done lifting a barbell

MATH 152: Work Exercise 2

Calculating the work done lifting a weight

MATH 152: Integration by Parts Exercise 2

Solving a definite integral with an exponential function using integration by parts

MATH 152: Integration by Parts Exercise 7

Solving a definite integral with arctangent using integration by parts

MATH 152: Trigonometric Integrals Exercise 4

Using a trigonometric identity to integrate powers of sine and cosine

MATH 152: u-Substitution Exercise 2

Using u-substitution to evaluate a definite integral with a power of a polynomial in the denominator

MATH 152: u-Substitution Exercise 3

Using u-substitution to integrate a rational function

MATH 152: u-Substitution Exercise 4

Using u-substitution to evaluate a definite integral with a natural logarithm

MATH 152: u-Substitution Exercise 6

Using u-substitution on an indefinite integral with an exponential function, sine, and cosine

MATH 152: Partial Fraction Decomposition Exercise 2

Using partial fraction decomposition to rewrite and then integrate a rational function

MATH 152: Partial Fraction Decomposition Exercise 6

Using partial fraction decomposition to rewrite and then integrate a rational function

MATH 152: Trigonometric Substitution Exercise 5

Using trigonometric substitution to evaluate a definite integral

MATH 152: Trigonometric Substitution Exercise 6

Using trigonometric substitution to evaluate a definite integral

WIR 20B M152 V36

Determining if an improper integral converges or diverges

WIR 20B M152 V37

Determining if an improper integral converges or diverges

WIR 20B M152 V38

Determining if an improper integral converges or diverges

WIR 20B M152 V39

Determining if an improper integral converges or diverges

WIR 20B M152 V40

Using the comparison test to determine if an improper integral converges or diverges

WIR 20B M152 V41

Using the comparison test to determine if an improper integral converges or diverges

WIR 20B M152 V42

Using the comparison test to determine if an improper integral converges or diverges

WIR 20B M152 V43

Using the comparison test to determine if an improper integral converges or diverges

MATH 152: Improper Integrals Exercise 1

Solving an improper integral where the upper limit of integration is infinity

MATH 152: Improper Integrals Exercise 2

Solving an improper integral where the upper limit of integration is infinity

MATH 152: Improper Integrals Exercise 3

Solving an improper integral where the upper limit of integration is infinity

MATH 152: Improper Integrals Exercise 4

Solving an improper integral where the upper limit of integration is infinity

MATH 152: Improper Integrals Exercise 5

Solving an improper integral where the upper limit of integration is infinity

MATH 152: Improper Integrals Exercise 6

Solving an improper integral where the upper limit of integration is infinity

MATH 152: Improper Integrals Exercise 7

Solving an improper integral where the lower limit of integration is negative infinity

MATH 152: Improper Integrals Exercise 9

Solving a type two improper integral with a limit

MATH 152: Improper Integrals Exercise 10

Solving a type two improper integral using a limit

MATH 152: Improper Integrals Exercise 11

Solving a type two improper integral using a limit

MATH 152: Improper Integrals Exercise 12

Using the Comparison Theorem to solve an improper integral

MATH 152: Improper Integrals Exercise 13

Using the Comparison Theorem to solve an improper integral

MATH 152: Improper Integrals Exercise 14

Using the Comparison Theorem to solve an improper integral

Definite Integrals: MATH 171 Problems 5-9

The definition and properties of definite integrals

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

Using Reimann sums and the Fundamental Theorem of Calculus

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

Using Riemann sums and the Fundamental Theorem of Calculus

Integration by Substitution: MATH 151 5.5 Problems 13 & 14

Examples of integration by substitution

Integration by Substitution: MATH 171 Problems 4-6

Using u substitution to evaluate integrals and prove facts about logarithms and integrals and

Definite Integrals: MATH 172 Review

Review of the definition of a definite integral

Review for the Common Exam: MATH 152 Exam 1 a Review Problems 1-4

Reviewing u-Substitution

Review for the Common Exam: MATH 152 Exam 1 b Review Problems 29-33

Review of trigonometric substitution

Review for the Common Exam: MATH 152 Exam 1 b Review Problems 34 & 35

Review of partial fractions

Review for the Common Exam: MATH 152 Exam 3 b Review Problems 4 & 5

Review of using tests to determine if a series is absolutely convergent, convergent, and divergent

Review for the Common Exam: MATH 152 Exam 3 c Review Problems 10-13

Review of power series properties and writing functions as power series

Review for the Common Exam: MATH 152 Exam 3 c Review Problems 13-18

Review of Taylor and Maclaurin Series and their properties

Review for the Common Exam: MATH 152 Exam 3 c Review Problems 4 & 5

Review of using tests to determine if a series is absolutely convergent, convergent, and divergent

Area with Riemann Sums and the Definite Integral

The definition of the Riemann Sum and how it relates to a definite integral

Area Between Curves

Using Riemann sums to find the definite integral for the area between curves

Integrating Along y-axis for Area Between Curves

Determining whether its easier to integrate along the \(x\) or \(y\)-axis to find the area between curves

Area Between Curves Using Multiple Integrals

Using multiple integrals to find the area between two curves

Area Between Curves: MATH 172 Problems 1-3

Interpreting integrals to represent areas between curves

Volume of a Solid: MATH 172 Problems 4-6

Using the disk and washer method to calculate the volume of rotational solids

Cylindrical Shell Method: MATH 172 Problems 1-3

Using cylindrical shells to calculate the volume of a rotational solid

Deriving the Formula for Cylindrical Shells

Deriving the formula for the method of cylindrical shells

Cylindrical Shells when Revolving Around y-axis

Explaining how to use cylindrical shells when the region is rotated around the \(y\)-axis

Definition of Work

Explaining the definition of work for constant and non-constant forces

Work Done Pulling Up a Rope

How to calculate the work done in lifting up a rope possibly with a mass

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

Calculating the average value of a function and proving the Mean Value Theorem for Integrals

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

Deriving and using the formula for the arc length of a curve

Hydrostatic Force: MATH 172 Problems 6 & 7

Using Riemann Sums and Integrals to calculate hydrostatic force

WIR2 20B M251 V10

Finding the length of a three-dimensional curve

WIR9 20B M251 V4

Using Green's Theorem to calculate the work done as a particle moves through a force field

WIR10 20B M251 V7

Using Stokes' Theorem to express a surface integral of the curl of a vector field as a single integral

Continuous Probabilities

Explaining how to calculate probabilities for continuous data using integrals

Probability Density Function Exercise 2

Solving for a constant so that a function is a probability density function

Uniform Probability

Explaining how to calculate probabilities for a uniform distribution

Introduction and Installation of Python

An introduction to installing and getting started with Python

Numerical Calculations in Python

Performing basic numerical calculations in Python

Creating and Manipulating Symbolic Expressions in Python

Creating symbolic expression in Python and then factoring, expanding, and simplifying the expressions

Using Variables in Python

Defining variables in Python and using the variables in equations

Plotting Expressions and Solving Equations Numerically in Python

Plotting an expression in Python and finding a numerical approximation for the solution

Plotting Multiple Expressions in One Graph in Python

Graphing a piecewise function using Python

Solving Equations Symbolically in Python

Solving equations symbolically in Python and interpreting the results

Tangents to Parametrized Curves at a Given Point in Python

Using Python to plot a parametrized curve and its tangent line at a point

Simplifying Difference Quotients in Python

Using Python to simplify a difference quotient and find a derivative using the limit definition

Parametric Plots and Tangents at a Given t-value in Python

Using Python to find the tangent line to a parametric equation and plot the two graphs

List Comprehension and Numerical, Graphical, and Symbolic Limits in Python

Using Python to numerically estimate a limit, graphically estimate a limit, and find the exact limit

List Comprehension and Patterns in Higher Derivatives in Python

Using Python's list comprehension tool to find several higher order derivatives of a function at once

Implicit Plots and Implicit Differentiation in Python

Using Python to plot an implicit curve and find a tangent line using implicit differentiation

Word Problems and the Algorithmic Process for Multistep Problem Solving in Python

Solving a multistep word problem in Python and graphing the resulting function

Finding Absolute (Global) Extrema in Python

Using Python to find the absolute maximum and minimum of a function on a closed interval

Finding and Graphing Tangent Lines to a Curve in Python

Using Python to find the equation of the tangent line to a curve and graphing the result

Finding Derivatives in Python

Finding derivatives in Python and solving for the rate of change of a force

Finding Horizontal Tangent Lines in Python

Finding when the tangent line to a function is horizontal in Python

Finding Intervals of Increase/Decrease and Concavity in Python

Using Python to find the intervals where a function is increasing or decreasing

For Loops and Recursive Sequences in Python

Using for loops in Python to generate a recursively defined sequence

Generating and Plotting Partials Sums of a Series in Python

Using Python to calculate the partial sums of a series to estimate the value of the series

Generating and Plotting Sequences in Python

Using Python to numerically, graphically, and analytically find the limit of a sequence

Plotting a Function and Partial Sums of its Power Series in Python

Video 29 in a series of Python instructional videos

Radius and Interval of Convergence in Python

Using Python to find the radius and interval of convergence of a power series with the Ratio Test

Probability Density Function Exercise 2

Solving for a constant so that a function is a probability density function