How do i calculate this definite integral???

[Riccardo]

Can someone tell me if i made some errors solving this integral? if not then how do i solve it on the interval ( pi/2 ; 0 ) ?

when i substitute x with pi/2 i get -infinite + infinite and that's where i get stuck.

Thanks in advance !

 

[Dr.Peterson]

Can someone tell me if i made some errors solving this integral? if not then how do i solve it on the interval ( pi/2 ; 0 ) ?

when i substitute x with pi/2 i get -infinite + infinite and that's where i get stuck.

Thanks in advance !

I didn't try to follow the details of your work; my result looks different.

What I did was to first rewrite sin(2x) using the double angle formula, rather than wait until later; then I did a substitution for cos(x) before using parts. This was a lot easier, I think.

But at the end, you know you'll have an improper integral, so you'll have to use limits. I presume you've learned about those.

 

[Riccardo]

I didn't try to follow the details of your work; my result looks different.

What I did was to first rewrite sin(2x) using the double angle formula, rather than wait until later; then I did a substitution for cos(x) before using parts. This was a lot easier, I think.

But at the end, you know you'll have an improper integral, so you'll have to use limits. I presume you've learned about those.

omg thank u so much i finally did it I already tried the double angle formula from the start but then i didn't think about a substitution. This was way easier than i expected thanks again