- #1
VantagePoint72
- 821
- 34
Hello,
I'm currently learning integration by trig substitution. The problem is:
integral ( x^2/sqrt(16-x^2) ) dx.
I seem to be having some difficulty...this is what I have:
let x=4sinu
dx = 4cosu du
Thus, we have:
integral 16sin^2(u)*4cosu du/(4cos^2(u)) (the last part is from the trig identity sin^2x + cos^2x = 1)
But now what? I simplied that as much as I could and then used integration by parts, but I ended up with the wrong answer. The correct answer is 8arcsin(x/4) - 0.5x*sqrt(16-x^2). Have I made a mistake in what I've done so far? If not, where do I proceed?
Thanks,
LOS
I'm currently learning integration by trig substitution. The problem is:
integral ( x^2/sqrt(16-x^2) ) dx.
I seem to be having some difficulty...this is what I have:
let x=4sinu
dx = 4cosu du
Thus, we have:
integral 16sin^2(u)*4cosu du/(4cos^2(u)) (the last part is from the trig identity sin^2x + cos^2x = 1)
But now what? I simplied that as much as I could and then used integration by parts, but I ended up with the wrong answer. The correct answer is 8arcsin(x/4) - 0.5x*sqrt(16-x^2). Have I made a mistake in what I've done so far? If not, where do I proceed?
Thanks,
LOS