Homework SourseFind the area of the region bounded by the given curve r9eth
Find the area of the region bounded by the given curve r=9e^(theta) on the interval (6/9)pi less than or equal to theta less than or equal to 2pi
Solution
The formula for the area is the integral from a to b of 1/2 r^2 dtheta. So let\'s plug it in: [Note: I\'ll use t for theta] [integral from (6/9) pi to 2pi of] (1/2)(9e^(t))^2 dt = (1/2)[integral from (6/9)pi to 2pi] 81 e^(2t) dt = (81/2)*(1/2)*e^(2t) from (6/9)pi to 2pi = (81/4)(e^(4pi) - e^(12pi/9)
