# What is the integral of #sqrt(9-x^2)#?

##### 1 Answer

Whenever I see these kind of functions, I recognize (by practicing a lot) that you should use a special substitution here:

This might look like a weird substitution, but you're going to see why we're doing this.

Replace everyhting in the integral:

We can bring the 3 out of the integral:

You can factor the 9 out:

We know the identity:

If we solve for

This is exactly what we see in the integral, so we can replace it:

You might know this one as a basic antiderivative, but if you don't, you can figure it out like so:

We use the identity:

Now, all we have to do is put

To get

Now we need to insert it into our solution:

This is the final solution.