prob3intparts - ) g ( x ) dx = 4 , f (1) = 4 , f (3) = 2 ,...

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Math151Spr ing2008Gevec i Problem Set # 3 Integration by Parts Starred Problems are due on Friday, February 8 In problems 1-13, determine the inde f nite integral: 1*. Z xe 2 x dx 2. Z x 2 e x/ 3 dx 3. Z x cos μ 1 2 x dx 4*. Z x 2 sin μ 1 4 x dx 5*. Z x sinh ( x ) dx 6. Z x 2 cosh ( x ) dx 7*. Z arccos( x ) dx 8. Z arctan( x/ 2) dx 9. Z x 2 ln ( x ) dx 10*. Z ln( x ) x 1 / 3 dx 11. Z e x sin ( x ) dx 12. Z e x/ 4 sin (4 x ) dx 13*. Z e x cos ³ x 2 ´ dx In problems 14 and 15 evaluate the integral (simplify as much as possible): 14. Z 2 π π x cos (3 x ) dx 15*. Z e 2 e x 2 ln 2 ( x ) dx In problems 16 and 17, evaluate the integral by applying the de f nite integral version of integration by parts: 16. Z 3 / 2 1 / 2 arccos ( x ) dx 17*. Z 1 / 2 1 / 4 x sin ( πx ) dx 18*. Assume that Z 3 1 f
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Unformatted text preview: ) g ( x ) dx = 4 , f (1) = 4 , f (3) = 2 , g (1) = 4 , g (3) = 2 . Evaluate Z 3 1 f ( x ) g ( x ) dx. 1 19. Assume that f 00 and g 00 are continuous on the interval [ a, b ] , f ( a ) = g ( a ) = 0 , and f ( b ) = g ( b ) = 0 . Show that Z b a f 00 ( x ) g ( x ) dx = Z b a f ( x ) g 00 ( x ) dx. 20*. Assume that f 00 is continuous on the interval [ a, b ] and f ( a ) = f ( b ) = 0 . Show that Z b a f ( x ) f 00 ( x ) dx = Z b a ( f ( x )) 2 dx. 2...
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This homework help was uploaded on 04/21/2008 for the course MATH 151 taught by Professor Geveci during the Winter '08 term at San Diego State.

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prob3intparts - ) g ( x ) dx = 4 , f (1) = 4 , f (3) = 2 ,...

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