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August 31st, 2013, 10:29 AM   #1
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Need help with integration

I have a problem, I can't seem to figure out how to integrate (tan(x))^2. So far we've only been taught how to find basic antiderivatives and how to use substitution method. I've tried to look at the problem both ways, and I just can't seem to figure it out.

Its a problem where we are required to find the volume of an object by taking a curve and rotating it around an axis.

After reducing it to a simpler form, the integral looks like: the integral 9?[tan^2(?x/6)] from 0 to 1.

Can anyone give me a step-by-step walkthrough on integrating tan^2(x)? The rest of the problem and how to set it up to find the volume isn't an issue for me, that makes since. I just can't seem to figure out how to integrate tan^2(x), at least by using only my current knowledge, which is by using either basic antiderivatives and/or substitution method.
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August 31st, 2013, 10:34 AM   #2
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Re: Need help with integration

Have you tried to use this ?
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August 31st, 2013, 10:34 AM   #3
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Re: Need help with integration

Use the Pythagorean identity:



Now it should be a piece of cake.
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August 31st, 2013, 11:53 AM   #4
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Re: Need help with integration

Lol. I got it now. Thanks guys. Those blasted trigonometric identities always sneak up on me!
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