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Math 152 WI10 Exam 1 Review with Solutions

# Math 152 WI10 Exam 1 Review with Solutions - MSLC Math 152...

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MSLC – Math 152 Exam 1 Review 1) Verify the following integrals give the indicated result. a. ( ) ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) 1 1 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 10 5 10 10 ( ) 5 10 10 2 5 5 10 ( ) (5 ) 5 10 5 5 5 5 5 10 10 10 (5 ) (5 ) 10 25 5 50 5 25 1 25 10 25 10 10 dx x x c x x x x x x f x c x x x x x x x f x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x = − + = − + = − = − = − + = − = − = b. 1 1 2 2 1 1 2 2 2 2 ( ) 2 ( ) 2 x x x x x x x x x x x x c c e e e e dx e e f x e e c e e f x e e + + = + = + = + + = = c. 2 2 2 ln 1 ln 1 1 ( ) ln 1 ln 1 1 1 ( 1) ( 1) 2 ( ) 1 1 ( 1)( 1) 1 dx x x C x f x x x C x x f x x x x x x = + + = + + + = = = + + d. 2 2 2 2 1 ( 1) 1 1 ( ) 1 ( 1) ( 1) 2 ( ) ( 1) ( 1) x x x x x x x x x x x x x e e dx C e e e f x C e e e e e e f x e e = + + + = + + + = = + +

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