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Mathematics LibreTexts

5.6 Notes

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  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    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.


    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, evaluation theorem) we can evaluate a definite integral by evaluating the antiderivative of the integrand at the endpoints of the interval and subtracting
    mean value theorem for integrals
    guarantees that a point c exists such that \(f(c)\) is equal to the average value of the function


    • 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