CK12 Calculus - Single Variable

Use integrationby partsmethodto compute

Solution:
We note that our othersubstitutionmethodis not applicablehere.But our integrationby partsmethodwill
enableus to reducethe integraldownto one that we can easilyevaluate.

Let and then and
By substitution,we have

We can easilyevaluatethe integraland have

And shouldwe wish to evaluatedefiniteintegrals,we needonly to applythe FundamentalTheoremto the
antiderivative.

LessonSummary

1. We integratedcompositefunctions.


2. We usedchangeof variablesto evaluatedefiniteintegrals.


3. We usedsubstitutionto computedefiniteintegrals.

ReviewQuestions
Computethe integralsin problems#1–10.