convert int int dx dy to polar coordinates integral

[stars584]

∫ ∫ dx dy

Limits:

-√ (a2 – x2) ≤ y ≤ √ (a2 – x2)

-a ≤ x ≤ a

Conversion

∫ ∫ r dr dθ

Limits:

0 ≤ y ≤ a

0≤ x ≤ ∏

(R^2)/2 = (a^2)/2 = ( ∏a^2)/2

What did I do wrong.. the answer should be ∏a^2.

 

[galactus]

The x limits should be 0 to 2Pi, not 0 to Pi.

2Pi is a complete circle. 0 to Pi would only be a semicircle, 1/2, which is what you have.


\(\displaystyle \L\\\int_{0}^{2\pi}\int_{0}^{a}rdrd{\theta}\)