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Find the center of mass of the homogeneous lamina bounded by x = pi/4, x=3pi/4, y = 0, f(x) = sin(x).

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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Question

Find the center of mass of the homogeneous lamina bounded by

x = pi/4, x=3pi/4, y = 0, f(x) = sin(x).

Expert Solution

Step 1

Centre of mass = $x$ = My/A , $y$ = Mx/A

A= $\int_{a}^{b}$ [f(x)]-g(x)dx

My = $\int_{a}^{b}$ x[f(x)-g(x)]dx

Mx = $\int_{a}^{b}$ 1/2[f²(x) - g²(x)]dx

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