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fk378
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Homework Statement
Find the volume of the solid given the following:
y=x^2
y=0
x=1
x=2
revolved about x=4
Homework Equations
Shell method: 2pi(x)([f(x)] dx
The Attempt at a Solution
I shifted the function left 4 units, so I replaced x's with x+4
This makes the new functions:
y=(x+4)^2
y=0
x=-3
x=-2
Using -2 and -3 as the bounds, I have the integral of 2(pi)x (x+4)^2 dx, which is to say 2(pi)x (x^2 + 8x + 16)dx, which equals 2(pi)(x^3 + 8x^2 + 16x)
Integrating I get:
2(pi) [(x^4)/4 + (8x^3/3) + (16x^2/2)]
After evaluating it from -3 to -2, I get a negative value.
However, the right answer is supposed to be 67(pi)/6
Anyone think they can catch what's wrong?
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