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Integration by parts

  • #1

Homework Statement



[tex]\int[/tex] t sin(2t) dt

Homework Equations



Integration by parts formula:

[tex]\int[/tex]udv = uv - [tex]\int[/tex]vdu

The Attempt at a Solution



I chose t to be u so,

u=t
du=dt
dv=sin(2t)dt
v=(sin)^2 (hope that's right. I used double angle formula to change sin(2t) into 2sint cost)

So now by the integration by parts formula I get:


[tex]\int[/tex]t sin(2t)dt = t(sint)^2 - [tex]\int[/tex](sint)^2 dt

Now I have no idea how to integrate sin2t

I don't know if I messed up somewhere way up there or if it's right and I'm just stuck on this part. Any help would be greatly appreciated. Thanks in advance!

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,258
618
You integrate sin(t)^2 by using the double angle approach again. But the whole thing is a lot easier if you integrate sin(2t) just using the substitution u=2t.
 
  • #3
Wow thanks Dick I can't believe I overlooked that. Also, thanks a lot for the prompt reply!
 

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