correct, i want to compute the area of the oval type shape in the middle.
i took the integral with 0 ≤ r ≤ 2sin(θ) 0≤ θ ≤ ∏/2
∫∫ (r2cosθ) dr dθ
and got 2/3
then i took the integral
(5/6)∏ ≤θ ≤ ∏ 0 ≤ r ≤ 2sinθ
∫∫(r2cosθ) dr dθ
and got -1/24
i took the...
i see it more of as, computing 0 to pi/2 and having my upperbound be my bottom circle.
and then computing 0 to pi/6 and having my upperbound be my top circle.
subtracting the second from the first and then doubling it.
im looking at it now. could i use simple geometry to find the intervals of theta?
Pythagorean theorem to get the angle on each side with respect to the x axis?
Homework Statement
The domain D is the intersection of two disks x^2 +y^2 = 1 and x^2 + (y-1)^2 =1
use polar coordinates to find the double integral ∫∫(x)dA
Homework Equations
x = rcosθ y = rsinθ r^2 = x^2 + y^2
The Attempt at a Solution
I have drawn the circles...