CK12 Calculus - Single Variable

where
Giventheserulestogetherwith Theorem4.1, we will be able to solvea greatvarietyof definiteintegrals.
Example2:

Compute
Solution:

Example3:

Compute
Solution:

LessonSummary

1. We usedantiderivativesto evaluatedefiniteintegrals.


2. We usedthe MeanValue Theoremfor integralsto solveproblems.


3. We usedgeneralrulesof integralsto solveproblems.

Proofof Theorem4.1

We first needto divide into sub-intervalsof length. We let

be the endpointsof thesesub-intervals.

Let be any antiderivativeof