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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

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

Integral and Comparison Tests: MATH 172 Problems 4-7 thumbnail

Integral and Comparison Tests: MATH 172 Problems 4-7

Proving the Integral, Comparison, and Limit Comparison Tests

Comparison TestConvergent SeriesDivergent SeriesIntegral TestLimit Comparison TestMonotone Sequence TheoremPartial Sum of SeriesPartition of an IntervalRiemann Sum

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

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

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

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

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

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

Area Between CurvesAverage Value of a FunctionDefinite IntegralMean Value Theorem for IntegralsPartition of an IntervalRiemann Sum

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

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

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

Arc Length of a CurveDefinite IntegralMean Value TheoremPartition of an IntervalRiemann SumTrig Substitution