A lamina in the first quadrant is bounded by y = sin^−1(x), y =π/2, and the coordinate axes. If the density at any point (x, y) in the lamina is f(x,y) = x, find the y-coordinate of the center of mass of the lamina.

A lamina in the first quadrant is bounded by y = sin^−1(x), y =π/2, and the coordinate axes. If the density at any point (x, y) in the lamina is f(x,y) = x, find the y-coordinate of the center of mass of the lamina.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter8: Further Techniques And Applications Of Integration

Section8.3: Volume And Average Value

Problem 17E

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A lamina in the first quadrant is bounded by y = sin^−1(x), y =π/2, and the coordinate axes.
If the density at any point (x, y) in the lamina is f(x,y) = x, find the y-coordinate of the center of
mass of the lamina.

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