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# * OCR C4 Intergration question...* Hard! watch

1. Hey guys,

I am stuck once again.

i) Let I be the integral in this case... I cos^-1(x) with x=cos u

My workings....

if x=cosU
dx= -sinU

Therefore I cos^-1(cos(U)) * -sin U = I -Usin U

Now using integration by parts, You get UcosU - I Cos U

Now if cosU =x, then U = cos^-1(x)
Then, Cos^-1(x) * Cos(Cos^-1(x)) - Sin(Cos^-1(x))

Then you get XCos^-1(x) -Sin(Cos^-1(x))

The book says the answe is XCOS^-1(X) - SQRT* 1-X^2 +K

How the hell did they get that?

I am so confused
2. They're the same answer, since , which you can see by writing ; and here .
3. http://en.wikipedia.org/wiki/Inverse...tric_functions

Have a look at the relations in Section 2.
4. (Original post by nuodai)
They're the same answer, since , which you can see by writing ; and here .
ahh right I see thanks!

Just one quick question, without starting a new thread...

If U= e^x
then what would U be if it is e^-x?

Would it be 1/u?
5. (Original post by J DOT A)
ahh right I see thanks!

Just one quick question, without starting a new thread...

If U= e^x
then what would U be if it is e^-x?

Would it be 1/u?
If I understood what you said correctly, yes, .

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