Test 4a solutions

# Test 4a solutions - x is u = d-x d ` and hence the work is...

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Solutions for Test IV C1 I: a ) 1 5 ( x + 1) 5 - 1 4 ( x + 1) 4 + C b ) 2 5 ( x + 1) 5 / 2 - 2 3 ( x + 1) 3 / 2 + C c ) 1 3 exp( x 3 ) + C d ) 2 3 (2 3 / 2 - 1) + 2(2 1 / 2 - 1) The integral in e) vanishes since the integrand is odd. II: a) The two curves intersect at x = 0 and x = 2. hence the area is given by Z 2 0 ( x 2 - ( x 3 - x 2 ) ) d x = 4 3 b)The x coordinate of the centroid is determined by the integral Z 2 0 x ( x 2 - ( x 3 - x 2 ) ) d x = 8 5 which leads to x = 3 2 The y component of the centroid is determined by the integral Z 2 0 ( x 4 - ( x 3 - x 2 ) 2 ) d x which leads to y = 8 7 III: a) Denote by w = 20 the width, by ` = 50 the length, by d = 3 the maximal depth and by ρ = 1000 the density of water. The length of a layer of water at the depth

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Unformatted text preview: x is u = d-x d ` and hence the work is given by the integral gρ`w Z d x d-x d d x = g`wρd 2 6 = 1 . 5 × 10 7 J 1 b) The time it takes to empty the pool is 1 . 5 × 10 7 7 . 5 3 = 2000s which approximately 0 . 55 hours. IV: a) Slice parallel to the y axis. The volume is given by 2 π Z 1 x √ 1 + x d x = 4 π 15 (2 √ 2 + 1) b) Again, slice parallel to the y axis. The volume is given by the integral π Z 1 (1 + x )d x = 3 π 2 2...
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## This note was uploaded on 02/07/2011 for the course MATH 1501 taught by Professor N/a during the Fall '08 term at Georgia Institute of Technology.

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Test 4a solutions - x is u = d-x d ` and hence the work is...

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