Question

Graph r=1/(2cosθ) for −π/2<θ<π/2 and r=1. Then write an iterated integral in polar coordinates representing the area inside the curve r=1 and to the right of r=1/(2cosθ). (Use t for θ in your work.) With a=,b= c= and d= area =∫ab​∫cd​dd​ (b) Evaluate your integral to find the area. area = Note: You must complete part (a) in order to receive any partial credit.

Answer 1

To find the area inside the curves r=1 and r=1/(2cosθ), an iterated integral in polar coordinates is set up. The limits of integration for θ are 0 to π/2, and for r, it is from 1/(2cosθ) to 1. The area is found by evaluating the integral.

Step-by-step explanation:

To find the area inside the curve r=1 and to the right of r=1/(2cosθ), we can set up the iterated integral in polar coordinates. Since the region is to the right of the curve, the limits of integration for θ would be between 0 and π/2. The limits for r would be from 1/(2cosθ) to 1. So, the iterated integral representing the area is:

area = ∫0π/2 ∫1/(2cosθ)1 r dr dθ

To evaluate this integral, we integrate with respect to r first and then with respect to θ.