Integration by parts query. Getting 0 as answer, think its wrong, help!!

Hi,

I'm asked to integrate e^2xcosxdx. I have used intefration by parts letting u=e^2x and dv=cosxdx. This results in

e^2xsinx-the integral of 2sinxe^2x. I then integrated by parts again and the overall result was if I = integral of e^2xcosxdx then

I= e^2xsinxdx-e^2xsinxdx + 0.5( I)

0.5I = 0

Therefore I=0

Is this wrong?

Re: Integration by parts query. Getting 0 as answer, think its wrong, help!!

Quote:

Originally Posted by

**orlacoon** Hi,

I'm asked to integrate e^2xcosxdx. I have used intefration by parts letting u=e^2x and dv=cosxdx. This results in

e^2xsinx-the integral of 2sinxe^2x. I then integrated by parts again and the overall result was if -I = integral of e^2xcosxdx then

I= e^2xsinxdx-e^2xsinxdx + 0.5( I)

0.5I = 0Therefore I=0

Is this wrong?

You are making a sign error.

Add that last integral to both sides and then divide by 2.

Re: Integration by parts query. Getting 0 as answer, think its wrong, help!!

Still not sure where I'm going wrong. Could you explain further? Thanks

Re: Integration by parts query. Getting 0 as answer, think its wrong, help!!

You should end up with the same integration but with a minus sign on the right side. You move that integration to the left hand side and then divide by two.

So you should end up with something like:

I= .......... -I (move right hand integration to left hand side)

2I = .............. (divide by two)

I = 1/2(..........) (Final answer)

Sorry i didn't do the integration. In class right now =p

Re: Integration by parts query. Getting 0 as answer, think its wrong, help!!

Quote:

Originally Posted by

**Plato** You are making a sign error.

Add that last integral to both sides and then divide by 2.

He's right. Remember to pick the right u and v' elements.

Derivative of (sinx)' = cosx and (cosx)' = -sinx

Re: Integration by parts query. Getting 0 as answer, think its wrong, help!!

Re: Integration by parts query. Getting 0 as answer, think its wrong, help!!

Thanks a lot, got it wrong way around!