Evaluating an integral interpreted as area...

Finishing the last chapter of Calculus 1, so go easy on me you guys :|

I know this is like the easiest and most obvious thing. I just can't figure it out though; I need help.

I don't know why the answer is 6π.

Evaluate ∫ from -2 to 2 of (x + 3)(4 - x^2)1/2 dx by writing it as a sum of two integrals and interpreting one of those integrals in terms of an area.

Why? And how is this done?

Re: Evaluating an integral interpreted as area...

Now, note that is the semi unit circle of radius 2. Thus, the area is

Note, use direct subsitution to evaluate

Then and

Then = which equals zero.

Therefore,

Re: Evaluating an integral interpreted as area...

Omg :o

I have an exam on this stuff soon. This helped a lot!

Thank you :D