## David.Butler 2 years ago 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

1. JamesJ

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 $\int_0^{2\pi} \int_{r_2}^{r_1} r \ dr \ d\theta$

2. David.Butler

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.

3. JamesJ

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

4. JamesJ

Another good reason to draw the graph!

5. zepdrix

|dw:1359669259799:dw|Hmm I was trying to draw the graph :L it's pretty tricky though lol

6. zepdrix

|dw:1359669390955:dw|

7. zepdrix

The circle is drawn by the outer radius, so we subtract the inner radius from the outer.$\large \int\limits_{-\pi/3}^{\pi/3} 3a \cos x-(a \cos x+a) \quad dx$ Is the lower limit 5pi/3? I think it's -pi/3. a>0.. Hmm maybe not. Grr now I'm confusing myself :) lol

8. David.Butler

Oh no your right! Thanks , I kept doing the problem wrong , I was using the wrong bounds! Thanks So much

9. zepdrix

Ah ok cool c: