Recall the formula for a region whose boundary is given by a polar curve r=f(θ) and by the rays θ=a and θ=b.
A = ∫a b 1/z,2 dθ
We are given the area bounded by the graph of the polar equation r=e^−θ/12 that lies in the sector π/2 ≤θ≤π.
Therefore, the area of the region bounded by the given polar equation is as follows.