Question

Compute the following area.
The region inside one petal of the rose r =2cos3(theta). The answer pi, using limits of integration of double 0 to pi/2. Shouldn't the limits be pi/6 to pi/2?

Answer 1

i think limits should be 0 to pi/6 like you said. then double. but maybe they made a substitution like
\[\beta=3\theta\] and changed the limits at that point. so when
\[\theta=\frac{\pi}{6}\] you get
\[\beta=\frac{\pi}{2}\]

Answer 2

that is probably why the integral changed limits to from 0 to pi/2

Answer 3

How did you get 0 to pi/6?