Homework Help: Volume of solid curves

1. Apr 22, 2006

sparsh

Hi

Could someone please give me an idea on how to go about this problem

Find the volume of the curve genereated by revolving the area between the curve y =(cos x)/x and the x axis in the interval pie/6 to pie/2

Thanks a lot..

2. Apr 22, 2006

Tinaaa

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3. Apr 22, 2006

HallsofIvy

Better than a formula is to think through it: Draw a line from any point on the x-axis up to the curve. As the curve is rotated around the x-axis that line sweeps out a disk of radius y= cos(x)/x. It's area is $\pi y^2$ and if we imagine that as a very shallow cylinder of height dx (the height of the disk is in the x direction) its volume is $\pi y^2 dx$.
The volume of the whole thing is a sum of those volumes (a Riemann sum) and becomes the integral Tinaaa said:
$$\int_{\frac{\pi}{6}}^{\frac{\pi}{2}}y^2 dx$$
Since y= cos(x)/x, put that in and integrate.

Was this really for a PRE-Calculus course?

4. Apr 22, 2006

sparsh

@ Hallofivy

Thanks a lot. Actually I couldnt think up where to put this post so i just dropped it in Pre calculus.

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