## GR0568 #16

Forum for the GRE subject test in mathematics.
thmsrhn
Posts: 17
Joined: Fri Mar 26, 2010 7:18 am

### GR0568 #16

"Whatr is the volume of the solid formed by revolving about the x axis the region in the first quadrant of the xy plane bounded by co ordinate axes and the graph of the equation y=(1+x^2)^(-.5)?

origin415
Posts: 61
Joined: Fri Oct 23, 2009 11:42 pm

### Re: GR0568 #16

For volumes of solids of revolution, you want to create a new function corresponding to the cross-sectional area of the object, and integrate over that. Your function $$f(x)$$ corresponds to the radius, so your integral will be

$$\pi \int (f(x))^2 dx$$

mathQ
Posts: 41
Joined: Thu Mar 25, 2010 12:14 am

### Re: GR0568 #16

Volume = Int pi * y^2 dx | (inf, -inf)

with that ans should be pi^2

thmsrhn
Posts: 17
Joined: Fri Mar 26, 2010 7:18 am

### Re: GR0568 #16

I know rite?!, but that ain t the answer. it ((pi)^2)/2!!

joey
Posts: 32
Joined: Fri Oct 16, 2009 3:53 pm

### Re: GR0568 #16

Only the part in the first quadrant is revolved. Use
$$A=\pi \int_0^\infty \left[f(x)\right] ^2dx.$$

mathQ
Posts: 41
Joined: Thu Mar 25, 2010 12:14 am

### Re: GR0568 #16

Thanks joey.

the limit should be 0, Inf

with that ans is pi^2/2