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Antiderivatives

Antiderivatives. 5.1. Discovery of Power Rule for Antiderivatives. If f ‘ (x) = Then f(x) =. If f ‘ (x) = Then f(x) =. If f ‘ (x) = Then f(x) =. If f ‘ (x) = Then f(x) =. Differentiation. Integration. The process of finding a derivative. The process of finding the antiderivative.

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Antiderivatives

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  1. Antiderivatives 5.1

  2. Discovery of Power Rule for Antiderivatives If f ‘ (x) = Then f(x) = If f ‘ (x) = Then f(x) = If f ‘ (x) = Then f(x) = If f ‘ (x) = Then f(x) =

  3. Differentiation Integration The process of finding a derivative The process of finding the antiderivative Tells us the variable of integration Symbols: Integral Symbols: Integrand

  4. is the indefinite integral of f(x) with respect to x. Each function has more than one antiderivative (actually infinitely many) Derivative of: The antiderivatives vary by a constant!

  5. General Solution for an Indefinite Integral You will lose points if you forget dx or + C!!! Where c is a constant

  6. Basic Integration Formulas

  7. Find: You can always check your answer by differentiating!

  8. Basic Integration Rules

  9. Evaluate: C represents any constant

  10. Evaluate:

  11. Evaluate:

  12. Evaluate:

  13. Evaluate:

  14. Particular Solutions and F(1) = 0

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