|Feb15-12, 08:32 AM||#1|
People, today i had a exam in math analysis and there was a integral to solve:
∫ x^2√(1-x^2) dx
ok, i started to think about the trigonometric substitution. x= sint
but, with that substitution now i have a ∫sin^2tcos^2t dt
so i have to do something like ∫(1-cos^2t)(cos^2t) dt ok and i thought (no thanks...)
i never learned how to solve a integral with the trigonometric formula, so solve something like
∫cos^4t dt takes a lot of time.
So i tried t = √(1-x^2)
dt/dx = -x/(√(1-x^2) )
So now i have a integral
as we know t = √(1-x^2) so x= 1-t^2
-∫((1-t^2)t^2) dt = -∫t^2 - t^4 dt
ok now it is easy...
Please tell me that i did it in the correct way!
|Feb15-12, 09:00 AM||#2|
Blog Entries: 5
You can easily check by differentiating, however I think that you'll find you're off by a factor of x then.
The problem seems to be
I don't know how much that helps you though.
|Feb15-12, 09:08 AM||#3|
what a stupid error.
Damn. ok i should do it by trigonometric substitution.
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