# 5.6 Notes

- Page ID
- 13918

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Section 5.5 & section 5.6 are both on U-Substitution.

The exercises for sections 5.4 & 5.7 are just a handful.

All of sections of Chapter 5 are: section 5.1 through section 5.7.

## Glossary

**fundamental theorem of calculus**- the theorem, central to the entire development of calculus, that establishes the relationship between differentiation and integration

**fundamental theorem of calculus, part 1**- uses a definite integral to define an antiderivative of a function

**fundamental theorem of calculus, part 2**- (also,
) we can evaluate a definite integral by evaluating the antiderivative of the integrand at the endpoints of the interval and subtracting**evaluation theorem**

**mean value theorem for integrals**- guarantees that a point
*c*exists such that \(f(c)\) is equal to the average value of the function

### Contributors

Gilbert Strang (MIT) and Edwin “Jed” Herman (Harvey Mudd) with many contributing authors. This content by OpenStax is licensed with a CC-BY-SA-NC 4.0 license. Download for free at http://cnx.org.