Evaluate the integral by interpreting it in terms of areas

[phillyolly]

Homework Statement

The problem is in the attachment along with my answer. Can please one check if I got a correct answer?
Some sources say the answer is 2Pi instead of just Pi.

Homework Equations

The Attempt at a Solution

 

[Char. Limit]

I'm not sure where you got that your graph was a quarter circle. The shape is right, but you need to check your bounds...

 

[phillyolly]

That is because x cannot be less than 0. In the problem, we take a square root of it, so x is more or equal to 0.
Right?

 

[Char. Limit]

No, x can be less than zero. Your definite integral is from -2<x<2, after all. What is under your square root is not x, but 4-x^2. So 4-x^2 has to be greater than or equal to zero. Follow?

 

[phillyolly]

Please take look at a sample question in my book. I did my problem based on this example. I think I followed all its steps.

 

[Agent M27]

As Char limit has pointed out, they are similar in the fact that they deal with the graph of a circle, but check the bounds of the example problem and compare those with your problem, now think about how they differ.

Joe

 

[phillyolly]

Now I see, I didn't know that I should consider the bounds. Thank you, I got it.