# Homework Help: Volume of solid curves

1. Apr 22, 2006

### sparsh

Hi

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.