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 stepbystep 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 ? 
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: 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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