Question

Asked Sep 12, 2019

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Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the specified axis.

y = x^{3}, y = 8, x = 0, about x = 5

Step 1

Please see the attached diagram on the white board. Please see it crefully and locate the lines, curve and points of interest. Please see the point P (x, y)

x = 5 is the axis of rotation. The cylindrical shell will have a volume, dV = 2πrh.dx

h = 8 - y = 8 - x^{3}

r = 5 - x

Limits of integration will be x = 0 to x = 2

Step 2

hence, dV = 2π(5 - x)(8 - x3)dx

Pleas...

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