Evaluating an integral by pieces...

Question

amtran_bus · Answer

attachment

amtran_bus · Answer

Where am I wrong?
@cwrw238  @Agentjamesbond007 @agent0smith @Compassionate @jdoe0001 @lului @Luigi0210 @nubeer

phi · Answer

why did you type in  cosd theta  rather than cos theta?

amtran_bus · Answer

Good question. My bad.

amtran_bus · Answer

But do I need to do the substituion again or is that the only issue?

phi · Answer

I assume you did
u = 9$\theta$   du = 9 dθ
dv = cosθ  dθ      v= sinθ 

and did
$$ \int u\ dv = uv - \int v \ du $$

amtran_bus · Answer

Yes. Matches perfectly.

phi · Answer

so except for the extra d, your solution looks good

amtran_bus · Answer

Yay! The computer took it! I have one more question. If the last part would have been multiplied by something rather than a constant (9), like another sin theta, would I have had to do the substation twice?

phi · Answer

if you multiply by a function of theta, then it is definitely more complicated. In fact, we may have to use a different trick than integration by parts... it depends

amtran_bus · Answer

Ok. I was just wondering. My prof. said some of the problems I would have to substitute twice and one I would have to use algebra.

phi · Answer

when you get to that problem you probably will notice.  If you need, help you can post it.

amtran_bus · Answer

Ok. Thanks Phi!!!!!!!!!!!!!