how would one integrate by parts the following:
use the fact that sin^2 x = (1-cos2x)/2
from the formula cos2x=1-2sin^2 x
Tell me how you wrote that equation
[ tex]\int sin^2xdx[/tex ]
Click on the image (equation) and the TeX code comes up. See also:
Aslo this is not a forum for homeworks, https://www.physicsforums.com/showthread.php?t=44101
Post questions regarding homework and similar in the homework section.
Are you required to use integration by parts? As rsm said, there are simple and standard substitutions for [itex]sin^2(x)[/itex] and [itex]cos^2(x)[/itex].
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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