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Topic: CALCULUS stuck with a problem
Replies: 2   Last Post: Sep 26, 2014 5:21 AM

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Opal

Posts: 4
Registered: 7/29/14
CALCULUS stuck with a problem
Posted: Jul 30, 2014 12:10 AM
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The question is to find the volume of the region bounded by y = 5 and y = x + (4/x), rotated about x = -1.

I used the cylindrical shell method but my answer doesn't match the textbook answer.

My method:
y = 5 intersects the curve at x = 1 and 4.

V = integrate (2*pi*(x+1)*(x + (4/x)) dx from x = 1 to 4.
= 2*pi*integrate(x^2 + 4 + x + (4/x)) from 1 to 4
= 2*pi*[ (1/3)(x^3) + 4x + (1/2)(x^2) + 4ln|x| ] from 1 to 4
= pi*(81 + 8ln|4|)
which is clearly different from the given answer 8*pi*(3-ln4).

Where did I go wrong?



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