handout_12_02

# handout_12_02 - Z 2 1 x 2 e x 3 4 dx = 4 3 Z b a e u du 3...

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INTEGRATION BY SUBSTITUTION 1. Determine the following antiderivatives: (1) Z e x 1 - e 2 x dx (2) Z 1 0 x 2 (2 x 3 + 3) 5 dx (3) Z e 1 (ln x ) 2 x dx (4) Z 1 0 tan - 1 ( x ) 1 + x 2 dx Date : December 02, 2009. 1

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(5) Z cot( θ ) (6) Z 1 0 ( x - 1) tan( x 2 - 2 x ) dx (7) Z ln( r ) r (1 + (ln r ) 2 ) dr 2. Find a and b for which the following holds:
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Unformatted text preview: Z 2 1 x 2 e x 3 / 4 dx = 4 3 Z b a e u du. 3. Suppose R 12 g ( x ) dx = π . What is R 4 g (3 x ) dx . Can you explain this graphically? 2...
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handout_12_02 - Z 2 1 x 2 e x 3 4 dx = 4 3 Z b a e u du 3...

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