Question

Area between two polar curves?

Find the area inside the circle r = 3*a*cosx and outside the cardiod r = a*cosx + a, where a > 0

Answer 1

So always start with a diagram: I'll let you draw that. It's not too bad.

Call the first function r1. That is r1 = 3a.cos(theta) , and I assume by the way you meant to write theta, not x? And the second function r2.

Then the area is the integral
\[ \int_0^{2\pi} \int_{r_2}^{r_1} r \ dr \ d\theta \]

Answer 2

Why are the bounds for the second integral 0 to 2pi ? They intersect at pi/3 and 5pi/3.

Thanks , I truly appreciate the help.

Answer 3

Ah, good. In which case, that's the range of values for theta.

Answer 4

Another good reason to draw the graph!

Answer 5

Hmm I was trying to draw the graph :L it's pretty tricky though lol