Question

Area enclosed by one loop of r=3sin(5theta)

Answer 1

Hello,

`Area= \int\limits^a_b {\rho^2} \, d\theta`


`(1)/(2) \int\limits^{(\pi)/(5)} _0 {(3\ sin(5\theta))^2} \, d\theta\\\\ =(9)/(4) \int\limits^{(\pi)/(5)} _0 {(1-cos(10\theta))} \, d\theta\\\\ =(9)/(4) [\theta-(sin(10\theta))/(10)]^(\pi)/(5)} _0 \\\\ =(9\pi)/(20)`

≈1.41371669412