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 August 31st, 2013, 10:29 AM #1 Newbie   Joined: Mar 2013 Posts: 24 Thanks: 0 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.
 August 31st, 2013, 10:34 AM #2 Senior Member   Joined: Mar 2012 From: Belgium Posts: 654 Thanks: 11 Re: Need help with integration Have you tried to use this ? $\tan^2 (x)=\sec^2 (x) - 1$
 August 31st, 2013, 10:34 AM #3 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Need help with integration Use the Pythagorean identity: $\tan^2(\theta)=\sec^2(\theta)-1$ Now it should be a piece of cake.
 August 31st, 2013, 11:53 AM #4 Newbie   Joined: Mar 2013 Posts: 24 Thanks: 0 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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