Taken from Chapter 19, Question 15 of Calculus Made Easy from the online edition, here is the question verbatim:
Show that the radius of a circle, the area of which is twice the area of a polar diagram, is equal to the quadratic mean of all the values of r for that polar diagram.
I was quite confused how to begin approaching this but noted that a circle of area $A_{circle} = \pi*r^2$ must be twice $2 * A_{polar} = 2 * \frac{1}{2}* \int_{\pi/2}^{\pi^2} a^2cos^2x dx$, however when evaluating this integral I end up with 0. What approach is more appropriate to answering this question and its corresponding proof?
Remarks: I ask this after searching online over a few weeks and asking people I know. Second, the polar equation format I got from a BlackPenRedPen video that was solving an area of a polar diagram question.