sum8.2.14 - revolving the curve y = 1-x 2 , x 1 about the...

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Week 4 Homework: Pre-view 7.1 - 7.5 as needed on new homework 7.8 improper integrals (rest of cases) 8.2 surface areas (rotation about y -axis) 8.3 centroid (with sketch) 9.1 (no hw), 9.3 separable differential eqn. 8.1 arc length 10.1, 10.2 (start parametric curves)
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2 Homework notes: Until further notice, problems and schedule are from the Fall 2004 list. Problem 8.2.14: Find the surface area of the surface obtained by
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Unformatted text preview: revolving the curve y = 1-x 2 , x 1 about the y-axis. Solution: We use A = Z 2 x p 1 + ( y ) 2 dx. We have y =-2 x, so A = Z 1 2 x p 1 + 4 x 2 dx. Take u = 1 + 4 x 2 , then du = 8 x dx, so Z 2 x p 1 + 4 x 2 dx = 4 Z u 1 2 du = 4 2 3 u 3 2 + C = 4 2 3 (1 + 4 x 2 ) 3 2 + C. So A = h 6 (1 + 4 x 2 ) 3 2 i 1 = 6 (5 3 2-1) ....
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This note was uploaded on 02/29/2008 for the course MATH 22 taught by Professor Dodson during the Summer '05 term at Lehigh University .

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sum8.2.14 - revolving the curve y = 1-x 2 , x 1 about the...

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