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

y = sqrt x,      y = 0,     x = 1;    about x = −4
Jul 31st, 2015

given y = 8 sqrt x

so take integral from x = 0 to x = 1 (given)

Axis of rotation given = -4

formula for Surface area of cylindrical shell = 2π r h
r = distance = x - (-4) = x + 4

h = y = height = 8 sqrt x

v = 2π  integral from 0 to 1 [ r h] dx

v = 2π  integral from 0 to 1 [(x + 4) 8 sqrt x]  dx

v = 2π  integral from 0 to 1[ (8x^ (3/2) + 32x^ (1/2))] dx

So

v = 736 π/15

required volume =  736 π/15 answer

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Jul 31st, 2015

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Jul 31st, 2015
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Jul 31st, 2015
Oct 19th, 2017
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