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Homework 2 - Name Section MAC 2312 Homework 2 Due SHOW ALL...

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Name: Section: MAC 2312 Homework 2 Due February 21, 2012 SHOW ALL OF YOUR WORK L10: Strategy of Integration 1. Evaluate the indefinite integral integraldisplay e 2 x 1 + e x dx. 1
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2. Evaluate the indefinite integral integraldisplay 1 1 + 2 e x - e x dx 2
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3. Evaluate the indefinite integral integraldisplay 1 x + 3 x dx 3
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4. Find a function f ( x ) satisfying f ( x ) = radicalbig (1 + x ) / ( x - 1) for -∞ <x< - 1. 4
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5. Evaluate the indefinite integral integraldisplay sin(2 x ) radicalbig 9 - cos 4 ( x ) dx 5
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L11: Improper Integrals 6. Determine whether the definite integral is convergent or divergent. If the integral is convergent, find its value. If the integral is divergent, show why it is divergent. integraldisplay 1 0 x ln xdx 6
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7. Determine whether the definite integral is convergent or divergent. If the integral is convergent, find its value. If the integral is divergent, show why it is divergent. integraldisplay e 1 x (ln x ) 2 dx 7
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8. Determine whether the definite integral is convergent or divergent. If the integral is convergent, find its value. If the integral is divergent, show why it is divergent.
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