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
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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
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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