S stars584 New member Joined Nov 27, 2006 Messages 19 Mar 4, 2007 #1 ∫ ∫ 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.
∫ ∫ 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.
G galactus Super Moderator Staff member Joined Sep 28, 2005 Messages 7,203 Mar 4, 2007 #2 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. \(\displaystyle \L\\\int_{0}^{2\pi}\int_{0}^{a}rdrd{\theta}\)
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. \(\displaystyle \L\\\int_{0}^{2\pi}\int_{0}^{a}rdrd{\theta}\)
