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

2022
Views:

127

Pages:

1
Author:

Tyshawn Shaffer

COSMOS: Complete Online Solutions Manual Organization System Chapter 9, Solution 9. x2 y2 + =1 a 2 b2 x = a 1− y2 b2 dA = xdy dI x = y 2dA = y 2 xdy b b I x = ∫ dI x = ∫ − b xy 2dy = a ∫ − b y 2 1 − Set: y = b sin θ y2 dy b2 dy = b cosθ dθ π I x = a ∫ 2π b 2 sin 2 θ 1 − sin 2 θ b cosθ dθ − 2 π π − − = ab3 ∫ 2π sin 2 θ cos 2 θ dθ = ab3 ∫ 2π 2 2 1 2 sin 2θ dθ 4 π π 1 1 1 1  2 = ab3 ∫ 2π (1 − cos 4θ ) dθ = ab3 θ − sin 4θ  − 2 4 8 4  −π 2 = 1 3  π  π  π 3 ab  −  −   = ab 8  2  2  8 2 Ix = 1 π ab3 8

COSMOS Chapter 9 Solution 9

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