Help!!! Integration by parts... Watch

Rokaf0
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#1
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Okay the question is

8i) State the derivative of e^cosx

I got dy/dx= -sinxe^cosx

8ii) Hence use integration by parts to find the exact value of

Integral {1/2 pi and 0} cosxsinx e^cosx dx

Integration by parts usually involves only two subjects, how can I solve this one with three?
Any help would be greatly appreciated!
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ghostwalker
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(Original post by Rokaf0)
...
You just need to split it into 2 parts, and given the first part of the question, the obvious way to split it is

Integral {1/2 pi and 0} (cosx)(sinx e^cosx) dx
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steve10
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Do you remember the IBP formula?

What you are given is:\frac{dy}{dx}=-\sin{x}\cdot e^{\cos{x}}

And you have to integrate: \int_0^{\frac{\pi}{2}}u(x)\frac{  dv}{dx} dx

where u(x)=\cos{x} and \frac{dv}{dx}=\frac{dy}{dx}=-\sin{x}\cdot e^{\cos{x}}
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kitkat313
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You could say that cosxsinx = (1/2)(sin2x) and that would make it 2 parts.
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Rokaf0
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(Original post by kitkat313)
You could say that cosxsinx = (1/2)(sin2x) and that would make it 2 parts.
Thankyou! Didn't think of that... double angle formulae everywhere in core 4!
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Daniel Freedman
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(Original post by kitkat313)
You could say that cosxsinx = (1/2)(sin2x) and that would make it 2 parts.
No. Don't do this!

The first part of the question relates to the second part (as usual)
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imzir
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(Original post by Rokaf0)
Thankyou! Didn't think of that... double angle formulae everywhere in core 4!

(Original post by Daniel Freedman)
No. Don't do this!

The first part of the question relates to the second part (as usual)
Daniel is absolutely right.

Trust me its crystal clear if you use the first part as the integration formula requires you to know the derivative of one part.

you should get -(cosx +1)e^cosx i think
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Rokaf0
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Ohhh okay, yeah a lot of Core 4 Q's are solved that way too. Thankyou people
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kitkat313
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Sorry I didn't make myself completely clear.

Eurgh I know they crop up everywhere :/
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