This is problem 22 Section 6.5 page 405. This problem is concerned with finding

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This is problem 22 Section 6.5 page 405. This problem is concerned with finding the centroid (phi=1 ) of the planar region in the first quadrant bounded by the curves y=x^3 and y=cuberoot(x) . We solve this problem by finding the mass m, and the moments Mx and My. Then we obtain x=My/m y=Mx/m (A) The formula for the mass can be written as integrate H(x)dx from a to b where a= b= H(x)= Evaluating the integral we find m= (B) The formula for Mx can be written as integrate K(x)dx from a to b where K(x)= Evaluating the integral we find Mx= (C) The formula for My can be written as integrate L(x)dx from a to b where L(x)= My=

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