Homework Help: Integration by parts.

1. Dec 17, 2007

annamariesmit

how would one integrate by parts the following:
$$\int sin^2xdx$$

thanks!

2. Dec 17, 2007

rsm

answer

hi
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

3. Dec 18, 2007

malawi_glenn

4. Dec 18, 2007

HallsofIvy

Are you required to use integration by parts? As rsm said, there are simple and standard substitutions for $sin^2(x)$ and $cos^2(x)$.

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:
$$\int sin^2(x) dx= \int (sin(x))(sin(x) dx)$$
Let u= sin(x) and let dv= sin(x) dx. Then du= cos(x)dx and v= -cos(x)
$$\int sin^2 x dx= -sin(x)cos(x)+ \int cos^2(x) dx$$
Now do the same thing with that integral. Of course, what happens is you will get back to your original $\int sin^2(x) dx$- but with a lot of other things. Solve that equation algebraically for $\int sin^2(x)dx$

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