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Integration by parts. 
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#1
Dec1707, 11:51 PM

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how would one integrate by parts the following:
[tex]\int sin^2xdx[/tex] thanks! 


#2
Dec1707, 11:58 PM

P: 1

hi
use the fact that sin^2 x = (1cos2x)/2 from the formula cos2x=12sin^2 x Tell me how you wrote that equation 


#3
Dec1807, 03:52 AM

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[ tex]\int sin^2xdx[/tex ]
Click on the image (equation) and the TeX code comes up. See also: http://www.physicsforums.com/showthread.php?t=8997 Aslo this is not a forum for homeworks, http://www.physicsforums.com/showthread.php?t=44101 Post questions regarding homework and similar in the homework section. 


#4
Dec1807, 05:55 AM

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Integration by parts.
If you are required to use integration by parts, then, since integration by parts requires a product, the obvious thing to do it write this as a product: [tex]\int sin^2(x) dx= \int (sin(x))(sin(x) dx)[/tex] Let u= sin(x) and let dv= sin(x) dx. Then du= cos(x)dx and v= cos(x) [tex]\int sin^2 x dx= sin(x)cos(x)+ \int cos^2(x) dx[/tex] Now do the same thing with that integral. Of course, what happens is you will get back to your original [itex]\int sin^2(x) dx[/itex] but with a lot of other things. Solve that equation algebraically for [itex]\int sin^2(x)dx[/itex] 


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