My Math Forum notation and volume integration

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 February 20th, 2012, 05:03 PM #1 Newbie   Joined: Aug 2011 Posts: 25 Thanks: 0 notation and volume integration sorry if this is in the wrong section but i am doing a math problem which says f(x)=cosx and g(x)=secx for x ? ] -pi/2, pi/2 [ what are these reverse brackets? edit : i am having problem with this problem. Let R be the region enclosed by the two graphs. the Region r is rotated through 2pi about the x axis to generate a solid. a) write down an integral which represents the volume of this solid. b) hence find the exact value of the volume. i have tried to find the integral using the cylinder method, but i am having trouble. i have done integral of sec(x)*cos(x)*2*(2pi-x) although this is a dy problem and now i am stuck
February 21st, 2012, 02:33 AM   #2
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Re: notation and volume integration

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Quote:
 Let R be the region enclosed by the two graphs. the Region r is rotated through 2pi about the x axis to generate a solid. a) write down an integral which represents the volume of this solid. b) hence find the exact value of the volume.
If $f(x)=\cos(x)$ and $g(x)=\sec(x)$ with $x\in\left[-\frac{\pi}{2},\frac{\pi}{2}\right]$ and the rotation is made about the x-axis then you have to use the disc method,
$V=\pi\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left|\sec(x)^2-\cos(x)^2\right|\;dx$ but this integral does not converge![/color]

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the region s is rotated through 2pi

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