monroe17
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.
y=1/x^4, y=0, x=2, x=6, about y=4



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math>philosophy
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I would use the method of cylindrical shells. At any f(x) value between 2 and 6, what is the radius from that y point to y = 4?

ByteMe
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Which method u prefer? shell or washer?

monroe17
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I just need help setting it up to integrate then i can take it from there...

ByteMe
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The setup of the integral depends on the method you use....

monroe17
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^ I didn't see your comment.. the washer method :)

math>philosophy
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Why you choose washersssssss D:

monroe17
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isn't easier? or not? usually for me it is easier..

ByteMe
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i agree that washer is appropriate here....
hang on....

math>philosophy
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You guys have fun with that >_>

ByteMe
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dw:1361159214153:dw

ByteMe
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Can you give me the expression for R and r?

monroe17
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errr.. ;/ crap.

ByteMe
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???

ByteMe
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no... i don't think it's that.. :)

monroe17
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haha give me a sec

ByteMe
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consider this...dw:1361159501396:dw

monroe17
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would it be 1/x^44

monroe17
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squared

ByteMe
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for R, shouldn't it be 1/x^4 + 4 ???

monroe17
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  + .. err yeah my bad

ByteMe
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ok... you also agree that r = 4 (inner radius) ???

monroe17
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yupp it is

ByteMe
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so...
\(\large dV=\pi(R^2r^2)dx \)
so
\(\large V=\pi \int_2^6(R^2r^2)dx \)
you replace the expressions for R and r ....

ByteMe
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sorry... i gotta leave... :(

ByteMe
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i'm pretty sure what we have is correct....