Hi! I attempted to solve the following problems and I would really appreciate it if someone checks them and show me the exacts steps so I know where I went wrong. ( I forgot how to find the limits, please show me how) Thanks!

1) Write the Integral that represents the area of the shaded region shown in the figure (please see attachment) of the following equation.

r= 1- cos 2θ

My Answer: 1/2 ∫(1-cos2θ)^2 dθ with limits pi/2, 2pi (pure guess)

2) Find the area of the region by finding the limits and evaluating the integral

of the following equations:

a) One petal of r= cos 5θ

b) Interior of r= 1- sin θ

My answers:

a) limits: 0, pi/5

integral equation: 1/2 ∫ (cos 5θ)^2 dθ

area: pi/20 or 0.157

b) limits (these were a pure guess) : pi/6 , 5pi/6

integral equation: 1/2 ∫ (1- sinθ)^2 dθ

area: pi/6 or 0.523