Calculus 2: Trigonometric Substitution, using Z = tan(x/2)

[kiz]

1. The problem statement, all variables and given/known data

http://i35.tinypic.com/2e2jsc8.jpg

2. Relevant equations

http://i38.tinypic.com/25rlguf.jpg


3. The attempt at a solution

After substituting:

http://i37.tinypic.com/2cf7axc.jpg

Using
http://i35.tinypic.com/14wzxiw.jpg
http://i35.tinypic.com/2yo47qx.jpg

I'm stuck here:
http://i34.tinypic.com/dzlsp.jpg

I can't seem to find anything online about this substitution. Any help would be appreciated. thanks.

[twasnow]

1. The problem statement, all variables and given/known data

http://i35.tinypic.com/2e2jsc8.jpg

2. Relevant equations

http://i38.tinypic.com/25rlguf.jpg


3. The attempt at a solution

After substituting:

http://i37.tinypic.com/2cf7axc.jpg

Using
http://i35.tinypic.com/14wzxiw.jpg
http://i35.tinypic.com/2yo47qx.jpg

I'm stuck here:
http://i34.tinypic.com/dzlsp.jpg

I can't seem to find anything online about this substitution. Any help would be appreciated. thanks.

I am so glad I have no need to remember any of this. my computer does all the calculations for me :)

[Dick]

http://en.wikipedia.org/wiki/Tangent_half-angle_formula You seem to have turned a '2' into a 'z' in you dx derivation. And you would have to change the limits to 'z' limits instead of 'x' limits if you are going to stick with the variable z. Otherwise just find the indefinite integral in terms of z and change the function back to x.

[kiz]

http://en.wikipedia.org/wiki/Tangent_half-angle_formula You seem to have turned a '2' into a 'z' in you dx derivation. And you would have to change the limits to 'z' limits instead of 'x' limits if you are going to stick with the variable z. Otherwise just find the indefinite integral in terms of z and change the function back to x.

Okay, thanks for the help, I'm looking at the solution and it has 1 and \sqrt{3} for the bounds, but I do not get that when insert \frac{\pi}{3} and \frac{\pi}{2}.

EDIT:

I got it, guess im blind. Thanks again.