# Quiz-04-Keys - Name Quiz 4 Keys 1 4x 2 dx = 2 x4 x This is...

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Name: _______________________________ Quiz 4 - Keys 1. 2 4 2 ? 4 x dx x x + = + This is a straight u-sub problem where ( ) 2 4 2 1 u x x du x dx = + = + Therefore: 2 2 4 2 2ln( 4) 4 x dx x x C x x + = + + 2. 2 sin ? x x dx = Another straight u-sub problem where 2 2 u x du xdx = = Therefore: 2 2 2 1 1 sin sin (2 ) cos 2 2 x x dx x xdx x C = = + 3. 2 sin ? x x dx = by letting u x = to begin the Integration by Parts. u x = du dx = 2 sin dv xdx = 2 1 cos2 sin 2 sin 2 2 4 x x x v xdx dx = = = 2 2 sin 2 sin 2 sin 2 cos(2 ) sin 2 4 2 4 2 4 4 8 x x x x x x x x x x dx x dx x C = = + 4. sin 2 ? x e x = Note: You will need to perform repeated use of the Integration by Parts on this one.

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