How to solve the integral using integration by parts?

[learningphysics]

ok I do that, but my RHS is different to what you suggested in post 45
I get...

-1 + (3/2)(I(-4)(pi/2) - I(-4)(pi/4))
Where to from there?

Yeah, what you've written is right. I've fixed the integrals. It's from pi/4 to pi/2 as you've written.

 

[t_n_p]

Ok, so once that is done I change back to the integral form?

 

[learningphysics]

Ok, so once that is done I change back to the integral form?

yeah. You can also go straight to the integral form after substituting in n=-2... it's up to you...

The idea is to get \int_{\pi/4}^{\pi/2}{sin^{-4}(x)dx} in terms of \int_{\pi/4}^{\pi/2}{sin^{-2}(x)dx}

 

[t_n_p]

yeh, so once I get up to.. https://www.physicsforums.com/latex_images/14/1408407-0.png

Do I let n=0 and repeat process to solve for LHS?

 

[learningphysics]

yeh, so once I get up to.. https://www.physicsforums.com/latex_images/14/1408407-0.png

Do I let n=0 and repeat process to solve for LHS?

No. The left side can be solved directly... the integral of 1/sin^2(x) = -cot(x)...

 

[t_n_p]

oh, didnt think of that!

 

[learningphysics]

Did you finish the problem?

 

[t_n_p]

Yep! Thanks a bunch :D