Integration: Trig Substitution

[char808]

My apologies. I'm not proficient with latex, and it is bogging my computer down for some reason today.

Homework Statement

[tex]int[/tex]dx/[tex]\sqrt{(4-x^2)}[/tex] [0, 2/[tex]sqrt{2}[/tex]

Homework Equations

Trig Identity: a^2-a^2sin^2[tex]\theta[/tex]

The Attempt at a Solution

In the interest of my own sanity I am going to leave out the limits of integration, assume they are there. Can someone explain how I input them in latex?

x=2sin[tex]\theta[/tex]

[tex]\int[/tex] dx/[tex]\sqrt{4-2sin\theta}[/tex]

[tex]\int[/tex] dx/[tex]\sqrt{4cos^2\theta[/tex]

[tex]\int[/tex] dx/[tex]2cos\theta[/tex]

1/2 [tex]\int[/tex] dx/[tex]cos\theta[/tex]

1/2ln |[tex]sec\theta + tan\theta|[/tex]

New Limits will be restricted to [-pi/2, pi/2]

I know when I use the identity that changes the limits, but I'm not sure how to calculate them..I assumed since the substitution corresponding to the identity only works on that interval than those would be the new limits.

 

[lineintegral1]

If you have limits of integration (in this case, they are values on an interval along x), then you need to plug them into x in your substitution. Then, isolate theta and make those your new limits.