Polar Coordinates Problem?
r=1+3sin(4θ) from 0 ≤ θ ≤ 2π. Find the area it encloses. Set up any integrals and use the calculator to evaluate any integrals.
Thank You to any body that can help on this
More Questions From This User See All
Answers & Comments
Verified answer
I don't know what the "negative r" regions could mean, but I'll try anyway.
A = int(from 0 to 2π) dθ int(from 0 to (1+3sin(4θ))) r dr=
= int(from 0 to 2π) dθ (1+3sin(4θ))^2/2 =
= int(from 0 to 2π) [1/2 + 3 sin(4θ) + (9/2) sin^2(4θ)] dθ =
= (1/2)2π + (9/2) π = (11/2)π