Find the centroid of the semicircle of radius 1 with center at the origin lying

Question

Find the centroid of the semicircle of radius 1 with center at the origin lying in the first and second quadrants. Find the centroid of the quarter circle of radius 1 with center at the origin lying in the first quadrant. Find the centroid of the solid formed by revolving each region bounded by the given curves about the given axis. y = x3, y = 0, and x = 1 about the x-axis y = x3, y = 0, and x = 1 about the y-axis y = 3 - x, x = 0 and y = 0 about the x-axis y = 3 - 2x, x = 0 and y = 0 about the y-axis y = x2, x = 1 and y = 0 about the y-axis x2 + y2 = 1, x = 0 and y = 0 about the x-axis In Sections 6.4 and 6.5 we used moments to find centers of mass and centroids. Each moment was the product of the mass and its distance from some line. This case is called the

Explanation / Answer

int(y=x3) => y2/2 = x4/4+c

int(y=3-x) => y2/2=3x-x2/2+c

int (y=3-2x)= >  y2/2= 3x - x2 +c

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