1. ## Iterated Integral

Use an Iterated Integral to find the area of the region bounded by the graphs of the equation.

x^2+y^2=4 , x=0 , y=0

2. Setup:
$\int_0^4 \left(\int_0^{\sqrt{4-y^2}} dx \right) dy$

3. Originally Posted by asdf122345
Use an Iterated Integral to find the area of the region bounded by the graphs of the equation.

x^2+y^2=4 , x=0 , y=0
If $x^2 + y^2 = 4$

then $y = \pm \sqrt{4 - x^2}$.

Also note, that since you are bounded by $x = 0$ and $y = 0$, you are stuck in the first quadrant, so we only take the positive square root. Also note that in this region, we have $0 \leq x \leq 4$ and $0 \leq y \leq 4$.

Therefore we are trying to find

$\int_0^2{\sqrt{4 - x^2}\,dx}$.

4. Shouldn't it go from 2 to 0?

5. Originally Posted by asdf122345
Shouldn't it go from 2 to 0?
Yes, yes it should. For a much easier time, convert it to polar coordinates