# A tricky trig sub integral.

• Feb 9th 2011, 05:10 PM
DannyMath
A tricky trig sub integral.
Tricky for me at least:

integrate: 10x^2/sqrt(4x-x^2)

I worked it out to this:

30arcsin((x-2)/2)-5sin(2arcsin((x-2)/2))-20sqrt(4-(x-2)^2)+C

I got pretty close to the answer I know because when I asked Wolfram to differentiate this it gave me

5x^2/sqrt(4x-x^2)

Maybe I made a mistake reverting to x from theta? I was a bit confused about how to handle sin(2theta) even though I drew a diagram of the right triangle. That's why I wrote sin(arcsin...) which I'm not sure is correct? Any clarification is appreciated :)
• Feb 9th 2011, 05:12 PM
pickslides
While you were at the Wolfram site, you should've asked for a solution to your integral and at least look to see if your substitution is correct!
• Feb 9th 2011, 05:27 PM
DannyMath
The problem is the Wolfram site's answer is so convoluted and used techniques we haven't covered. I'm doing the problem again and I think I'm coming to the right answer though! :) We shall see.
• Feb 9th 2011, 05:30 PM
DannyMath
Yes I made a mistake somewhere along the way. The answer is

60arcsin((x-2)/2)-10sin(2arcsin((x-2)/2))-40sqrt(4-(x-2)^2)+C

Thanks for the suggestion!