# Module_4_Mastery_Assignment_1375ea21-cb0d-49b6-bfa4-2ff2b97a157f

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Published on November 13, 2018

Author: mfoglio10

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Module 4 Mastery Assignment: Matteo Foglio Module 4 Mastery Assignment Topic 1 – Integration by Substitution: Integrating by substitution is used with u-substitution, which reverses differentiation performed with the chain rule. U-substitution is used when an integrand contains the product of a function and its derivative The inner equation, or g(x), is substituted as u General form: ∫f(g(x))g’(x)dx Steps to solve: 1. u=g(x), u’=g’(x)dx 2. ∫f(u)du 3. put back in terms of x: ∫ f(u)du=F(u)+C sub u=g(x) for F(g(x)) +C Topic 1 – Integration by Substitution Topic 1 Example: Topic 1 Example Topic 2 – Fundamental Theorem of Calculus: The fundamental theorem of calculus is the rule links a function and its derivative or antiderivative. If a function F(t) represents the rate at which something changes, then ∫f(x)dx represents the “total change” in the value. This concludes both ∫ f(x)dx=F(x) and F’(x)=f(x) We can also find that since F’(x)=f(x), You may likely be required to use u-substitution first before applying the fundamental theorem of calculus When applied, you will state the antiderivative in terms of x and evaluate it using limits of integration The antiderivative can also be found using u-substitution   Topic 2 – Fundamental Theorem of Calculus Topic 2 Example: Topic 2 Example

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