Find the area enclosed by one leaf of the rose r=5sin(5θ)

Answer 1

r=5sin5T

the rose has 5 petals

area = 1/2 integral of (5sin5T)^2 dT

use trig identities and u substitution

limits of integration are 0 and pi/5, where r=0

A = 5(pi/5 -(1/10sin2pi)= 5pi/5 + 0

area = pi= about 3.141593 square units