5.1 Antiderivatives and Indefinite Integrals.pdf - 5.1 Antiderivatives and Indefinite Integrals Objectives \u25aa \u25aa \u25aa The student will be able to

5.1 Antiderivatives and Indefinite Integrals.pdf - 5.1...

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1 5.1: Antiderivatives and Indefinite Integrals Introduction to Antiderivative If f (x) = x², then f(x) = _________________? If F (x) represents the “original” function, then we say F (x) = 3 is an antiderivative of the function f(x) = x² because F’ (x) = 𝑑 𝑑? ( ? 3 3 ) = However, there are many functions that have a derivative of f(x) = x², such as: In summary, antidifferentiation of a given function results in ________________________. In our example, we would write: ______________________________________________. The Indefinite Integral ?( ?)?? ∫ ?(?)?? = F(x) + C if F (x) = f(x) integral sign integrand constant of integration Antiderivative A function F is an antiderivative of a function f if: 𝑭 (𝒙) = 𝒇(𝒙) Objectives The student will be able to formulate problems involving antiderivatives. The student will be able to use the formulas and properties of antiderivatives and indefinite integrals. The student will be able to solve applications using antiderivatives and indefinite integrals.
2 Example: Find each indefinite integral a) ∫ 5?? b) ∫ 9? ?

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