Improper integrals

1. Feb 24, 2014

Chas3down

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

integral of 1/sqrt(9-x^2)
from 0 to 3

2. Relevant equations

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3. The attempt at a solution
I integrate it correct to arcsin(x/3) from 0 to 3
Get the correct anwser of pi/2.

But there is another question, At which value of x in the integration region [0,3] does special care need to be taken with the integration? I understand at some point it goes from negatie to positive, but i tried 0,3,pi/2,pi.. none worked.. anyhelp?

2. Feb 24, 2014

LCKurtz

What did you get when you put $x=3$ into the integrand?

And why do you say it goes from negative to positive?

3. Feb 24, 2014

scurty

Check the domain of the original function to be integrated.

4. Feb 24, 2014

Chas3down

I never had to do anything with the domain, it just worked.. But i guessed 0, pi/2 and 3. I thought it was be pi/2 because thats where it goes from neg to pos.

5. Feb 24, 2014

scurty

That's because you have been doing "proper" integrals up to this point. Improper integrals involve integrating across a point where the function is not defined. In this case the the function is not defined at x = __. The normal procedure is to introduce a variable for that number and take the limit as a approaches that number.

In this case, arcsin is defined on [0,1]. But the original function is not defined on [0,3].

6. Feb 24, 2014

LCKurtz

Try answering my two questions.