Calculus Help Please

Calculus
Tutor: None Selected Time limit: 1 Day

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

Thank you for the opportunity to help you with your question!

 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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