c2e1r - dx . 5. Compute Z 1 x arcsin x 2 dx . 6. Compute Z...

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Calculus II, Review Problems for Exam 1 September 25, 2007 1. Show that Z 1 0 dx ( x + 1)( x 2 + 1) = 1 4 ln 2 + 1 8 π . 2. Compute Z dx 2 e x + 1 . 3. Consider I = Z 1 0 1 9 sin x 2 dx . Find n (number of subdivisions) such that the trapezoidal rule estimate for I will be within 10 - 6 of the true value. (You may use the error bound K ( b - a ) 2 12 n 2 where K is an overestimate for the magnitude of the second derivative on the interval). 4. Compute Z x 2 x 3 + 5 x 2 + 8 x + 4
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Unformatted text preview: dx . 5. Compute Z 1 x arcsin x 2 dx . 6. Compute Z e 1 x 2 (ln x ) 2 dx . 7. Compute Z 1 x 2-x + 3 ( x + 1)( x 2 + 1) dx . 8. Compute Z 1 1 / 2 x x 2-2 dx . 9. Compute Z 4 3 dx ( x-1) 2 ( x + 1) . 10. Compute Z dx 1 + e x . 11. Compute Z ln( a 2 + x 2 ) dx , a 6 = 0 1 . 12. Compute Z sin( x + 1) dx . 2...
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c2e1r - dx . 5. Compute Z 1 x arcsin x 2 dx . 6. Compute Z...

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