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A03 - f 2 Evaluate the following(a Z 1-1 e x e x-1 dx(b Z...

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Math 138 – Fall 2011 Assignment 3 Due Friday October 7 (in the drop box by 12 noon) Hand in the following: 1. The curve f ( u ) = e u - u 4 - 1 has two roots u = 0 and u = b ( b > 0). Find the volume obtained when the region in the first quadrant bound by the curve x = e y - y 4 - 1 is rotated about the x -axis. You might want to use some plotting software to get an idea of the curve. Your answer should be in terms of the roots of
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Unformatted text preview: f . 2. Evaluate the following (a) Z 1-1 e x e x-1 dx (b) Z ∞ 1 √ x (1 + x ) dx Hint: a substitution will be required (c) Z ∞-∞ x 2 cos( x ) + 1 + cos( x ) 1 + x 2 dx 3. (a) For what values of k does the integral Z 1-1 | x | (1-x 2 ) k dx converge? (b) What is the value of the integral in (a) for the speciﬁc k that allow convergence?...
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