Expert: Paul Klarreich - 3/1/2010

Question
My question is as follows:

Evaluate the integral below by interpreting it as area and using formulas from geometry.

(integral from -8 to 8) of 2 times the square root of (64-x^2) dx.

I know the answer is supposed to be 64pi, but I keep getting 100.53, because the shape is a half circle with a radius of 8.
--> (1/2)(pi)(8)^2 = 100.53. Can you help me??

Answer
Questioner:    Leanna
Private: No
Subject:  Areas
Question: My question is as follows:

Evaluate the integral below by interpreting it as area and using formulas from geometry.

(integral from -8 to 8) of 2 times the square root of (64-x^2) dx.

I know the answer is supposed to be 64pi, but I keep getting 100.53, because the shape is a half circle with a radius of 8.

>> Yes, but you have a factor of '2' in there, which makes it the whole circle.  That should take care of it.

--> (1/2)(pi)(8)^2 = 100.53. Can you help me??