COSMOS Chapter 9 Solution 12 | Michigan State University

University:
Michigan State University
Course:
ERG 160 | Success in Science, Technology, Engineering, and Mathematics
Academic year:

2021
Views:

155

Pages:

1
Author:

Quintin Ware

COSMOS: Complete Online Solutions Manual Organization System Chapter 9, Solution 12. x2 y2 + =1 a 2 b2 y = b 1− x2 a2 dA = 2 ydx dI y = x 2dA = 2 x 2 ydx a a I y = ∫ dI y = ∫ 0 2 x 2 ydx = 2b ∫ 0 x 2 1 − x = a sin θ Set: x2 dx a2 dx = a cosθ dθ π I y = 2b∫ 02 a 2 sin 2 θ 1 − sin 2 θ a cosθ dθ 3 π 2 2 3 π = 2a b∫ sin θ cos θ dθ = 2a b∫ 02 2 0 π 1 2 sin 2θ dθ 4 π 1 1 1 1  2 = a3b∫ 02 (1 − cos 4θ ) dθ = a3b θ − sin 4θ  2 2 4 4  0 = 1 3 π  π a b  − 0  = a3b 4 2  8 Iy = 1 3 πa b 8