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Antiderivatives: MATH 171 Problems 4-6 thumbnail

Antiderivatives: MATH 171 Problems 4-6

Proving facts about antiderivatives and a physics application

AccelerationAntiderivativeAntiderivative of a FunctionDerivativeIndefinite IntegralInitial ConditionIntegralPositionVelocity
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Definite Integrals: MATH 171 Problems 5-9 thumbnail

Definite Integrals: MATH 171 Problems 5-9

The definition and properties of definite integrals

Area under a curveCircleDefinite IntegralIntegralLimitNorm of a PartitionPartition of an IntervalPolynomialRadiusRiemann SumRight EndpointsSquare Root
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Integration by Substitution: MATH 171 Problems 4-6 thumbnail

Integration by Substitution: MATH 171 Problems 4-6

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

CosineDefinite IntegralIndefinite IntegralIntegralLogarithmSineTrigonometryu substitution
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Definite Integrals: MATH 172 Review thumbnail

Definite Integrals: MATH 172 Review

Review of the definition of a definite integral

Area under a curveDefinite IntegralDefinite Integral RulesIntegrable FunctionIntegral RulesLimits of IntegrationPartition of an IntervalRiemann Sum
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Fundamental Theorem of Calculus and u-Substitution: MATH 172 Problems 4-7 thumbnail

Fundamental Theorem of Calculus and u-Substitution: MATH 172 Problems 4-7

Proving the Fundamental Theorem of Calculus and examples of u Substitution

Even FunctionFundamental Theorem of CalculusIndefinite IntegralIntegrable FunctionSecantTangentu substitution
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Area Between Curves: MATH 172 Problems 1-3 thumbnail

Area Between Curves: MATH 172 Problems 1-3

Interpreting integrals to represent areas between curves

AreaArea Between CurvesArea under a curveCosineDefinite IntegralPartition of an IntervalRiemann SumSineTrigonometryu substitution
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Volume of a Solid: MATH 172 Problems 4-6 thumbnail

Volume of a Solid: MATH 172 Problems 4-6

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

Definite IntegralDisk MethodPartition of an IntervalRiemann SumVolumeWasher Method
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Cylindrical Shell Method: MATH 172 Problems 1-3 thumbnail

Cylindrical Shell Method: MATH 172 Problems 1-3

Using cylindrical shells to calculate the volume of a rotational solid

Definite IntegralPartition of an IntervalRiemann SumShell Methodu substitutionVolume
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Calculating Work Using Integrals: MATH 172 Problems 4 & 5 thumbnail

Calculating Work Using Integrals: MATH 172 Problems 4 & 5

Using integrals to calculate work done in physics examples

Definite IntegralPartition of an IntervalRiemann Sumu substitutionWork
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