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Antiderivatives 5.1.

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Presentation on theme: "Antiderivatives 5.1."— Presentation transcript:

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

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

5 The antiderivatives vary by a constant!
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!

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

7 Basic Integration Formulas

8 You can always check your answer by differentiating!
Find: You can always check your answer by differentiating!

9 Basic Integration Rules

10 C represents any constant
Evaluate: C represents any constant

11 Evaluate:

12 Evaluate:

13 Evaluate:

14 Evaluate:

15 Particular Solutions and F(1) = 0


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