# U-sub and trig in Integral

1. Dec 15, 2007

### frasifrasi

For the integral from 0 to -sqrt(2)/2
of arcsin(x)/sqrt(1 - x^2)

I let u = arcsin(x) and the integral became the integral of u du.

Now, when I go to evaluate the limits of integration at arcsin(x) ^(2)/2 , there are two possible value of x that will give me the limit of integration in x <= 2pi, which one should I use and did I do anything wrong?

2. Dec 15, 2007

### Dick

No, the question says arcsin. And arcsin(-sqrt(2)/2) is a definite number, even though sin(u)=-sqrt(2)/2 has multiple solutions. The domain of arcsin is [-1,1] and the range is [-pi/2,pi/2].

Last edited: Dec 15, 2007
3. Dec 15, 2007

### frasifrasi

so, how do i do this? what does the integral evaluate to?

I am getting u^(2)/2...

4. Dec 15, 2007

### Dick

That's fine, or you can write it as (arcsin(x))^2/2. What's arcsin(-sqrt(2)/2)?

5. Dec 15, 2007

### frasifrasi

I guess I have to use the negative of pi/4 for the domain...

Last edited: Dec 15, 2007
6. Dec 15, 2007

### rocomath

I deleted that post!!! Can't believe you were able to quote it. I had just finished working out so I wasn't thinking right :p

7. Dec 16, 2007

### Dick

Guess I pounced too quickly. Sorry.