E4Review - Exam 4 Review MAC 2311 This is intended to be a...

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Exam 4 Review – MAC 2311 * This is intended to be a tool to help you review some of the material that could appear on the exam. It is not inclusive of all topics discussed in lecture. 1. Evaluate the following integrals: Z 1 ( x + 1) 2 d x Z e 4 x ( e 2 x - 4) 2 d x Z 3 tan(2 x )(sec(2 x ) - 1) d x Z e 4 1 ( ln( x ) ) 2 x d x Z ( x + 1 ) 2 x d x Z 5 0 | 9 - x 2 | d x Z 2 0 x e 1 - x 2 d x Z π 2 0 sin( x ) 3 p 1 + cos( x ) d x Z (1 + sin( x )) 2 cos 2 ( x ) d x Z e x ( e x + e ) 5 d x Z x 2 4 - x d x Z 5 x + 3 1 + x 2 - xe x 2 d x 2. True or false: a) Z x 1 g 0 ( t ) d t = d dx Z x 1 g ( t ) d t b) Z b a [ f ( t ) ] 2 d t = h Z b a f ( t ) d t i 2 3. The height (in meters) of water in a drainage pipe changes at a rate of γ ( t ) = 2 sin( t 2 ) cos 2 ( t 2 ) meters per hour. At t = 0 the height is 1 2 meters. Find the height of the water at every time t . 4. Find the area of the region on [ 0 , ln(81) ] bounded by the x -axis and the function f ( x ) = 18 + e 1 4 x x 4
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E4Review - Exam 4 Review MAC 2311 This is intended to be a...

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