- #1
ainster31
- 158
- 1
Homework Statement
Which of the following double integrals would correctly solve this problem?
Homework Equations
The Attempt at a Solution
I obtained two sets of boundary conditions.
Set 1:
$$x=-\sqrt{4-y^2}\quad (for\quad x<0)\quad to\quad x=\sqrt{4-y^2}\quad (for\quad x>0)\\y=-2\quad to\quad y=2$$
Set 2:
$$x=-2\quad to\quad x=2\\y=-\sqrt{4-x^2}\quad (for\quad y<0)\quad to\quad y=\sqrt{4-x^2}\quad (for\quad y>0)$$
This produces the following integrals:
$$\int_{-2}^{2}\int_{-\sqrt{4-y^2}}^{\sqrt{4-y^2}}(4-y)dxdy\\\int_{-2}^{2}\int_{-\sqrt{4-x^2}}^{\sqrt{4-x^2}}(4-y)dydx$$
So why aren't a, b, and c all correct? The correct answer is c. Why are a and b incorrect?