Find the area of the shaded region.

Question

r = sqrt 𝜃

A coordinate plane is given. A curve and a region are graphed.

1. The curve starts at the origin, goes counterclockwise becoming further away from the origin, passes through the positive vertical axis, passes through the negative horizontal axis, passes through the negative vertical axis, and stops on the positive horizontal axis.
2. The shaded region is inside the curve in the fourth quadrant.

Answer 1

r = √θ

1 . Area = (1/2)∫_{(0 to 2π)} r²dθ = (1/4)θ² evaluated from 0 to 2π = π²

For the second problem, evaluate from 3π/2 to 2π.