# Another Polar Coordinates + Integration Question

I came across this example on the net :

We are integrating over the region that is the area inside of r = 3 + 2 sin θ and outside of r = 2, working in polar coordinates (r,θ).

What is the limits of integration for θ?

# I already know the answer. But I have no idea how to arrive at the solution.

# Do I sketch r = 3 + 2 sin θ and r = 2? r = 2 is just circle centered at origin with radius 2. What about r = 3 + 2 sin θ?

LCKurtz
Homework Helper
Gold Member
Yes, you should plot them. The curves cross where they have equal r values. Set the r's equal and solve for theta. Then, using your picture to see which region is being asked for, set up an integral like this:

$$A = \int_{\theta_0}^{\theta_1} \int_{r_{inner}}^{r_{outer}} r dr d\theta$$

Check your picture and be sure you are integrating in the positive direction for theta.

Yes, you should plot them. The curves cross where they have equal r values. Set the r's equal and solve for theta. Then, using your picture to see which region is being asked for, set up an integral like this:

$$A = \int_{\theta_0}^{\theta_1} \int_{r_{inner}}^{r_{outer}} r dr d\theta$$

Check your picture and be sure you are integrating in the positive direction for theta.
How do I plot r = 3 + 2 sin θ without resorting to a graphing calculator? (and without knowing that equation represents a Limaçon)

Help! I just got to this site because i am looking for help with wind generators but can't figure out how to start a new thead.

can you help or direct me to where I need to go?

LCKurtz
Homework Helper
Gold Member
How do I plot r = 3 + 2 sin θ without resorting to a graphing calculator? (and without knowing that equation represents a Limaçon)
Make a table of values. For every 30 degrees (pi/6) value of theta plot r.

LCKurtz