Haven't Integrated in awhile. Assistance?

[Watterboy]

I haven't integrated in awhile. I still partially remember how do to it, but I could use some help integrating this pleasee: integrate from 0 to X. Integral of (squareroot(4-X^2)) dx

I remember that you have to make the squareroot a power of 1/2 and then add 1 to it. Then you divide by the new power. But I forget what you do with the inside of the parenthesis. I believe it is a substitution because it has a power, but I cant recall. You are integrating with respect to X

Thank youu

 

[galactus]

You can not integrate with respect to x and have it as an upper limit as well.

This is a 'dependent limit'. Make that upper limit of integration a y, a number, something besides an x.



\(\displaystyle \int_{0}^{?}\sqrt{4-x^{2}}dx\)

But, forget the limits for now.

To find the indefinite integral (without integration limits), you can use the sub

\(\displaystyle x=2sin(u), \;\ dx=2cos(u)du\). This is one way to go about it.

Remember the identity \(\displaystyle 1-sin^{2}(u)=cos^{2}(u)\)