Areas and Lengths in Polar Coordinates

[JSGhost]

Homework Statement

Find the area of the region enclosed by one loop of the curve.
r = sin(10θ)

I can't seem to get the correct answer...I checked every step. I was not sure what to integrate from but the polar graph of sin(10θ) should be similar to polar graph of sin(2θ). From pi/2 to 0?

Homework Equations

A = integral(b to a) (1/2)r^2 dθ

half angle formula
(sinθ)^2 = (1/2)(1-cos2θ)dθ

The Attempt at a Solution

A = integral(b to a) (1/2)r^2 dθ = integral(pi/2 to 0) (1/2)r^2 dθ

A = (1/2) integral(pi/2 to 0) (sin(10θ))^2 dθ
A = (1/2) integral(pi/2 to 0) (1/2)(1-cos(20θ))dθ
A = (1/4) integral(pi/2 to 0) (1-cos(20θ))dθ
A = (1/4) [(θ-(1/20)sin(20θ)] (pi/2 to 0)
A = (1/4) [(pi/2-(1/20)sin(20*(pi/2)) - (0 - 0)]
A = (1/4)* (pi/2) = pi/8

 

[JSGhost]

Nevermind. I figured it out. Integrating from pi/10 to 0. Thanks.