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Antiderivatives

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Definition: Antiderivative

We call F an antiderivative of f on the interval, I , ifD x F(x)=f(x) on I .

ie. If F'(x)=f(x) for all x on the interval.

Power Rule Theorem

For every real value of r except r = -1 , then

Indefinite Integral is a linear operator.

+ C

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EX 1 Evaluate the following integrals.

a)

b)

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EX 2 Evaluate the following integrals.

a)

b)

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Theorem

EX 3

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Generalized Theorem

Let g be differentiable and r a rational number, r ! -1 , then

EX 4

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EX 5

EX 6

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