Question

Find the area of the indicated region:

inner loop of r = 1 + 2 cos(theta)

how do I find out what the intervals for the integral are?

Answer 1

you need to set the curves equal to each other

Answer 2

how?

Answer 3

what is the other curve (or line) they gave you

Answer 4

just that. it's polar.

Answer 5

a polar equation.

Answer 6

1+2cos theta=0, calculate this

Answer 7

but dont worry about that just yet: On your sketch of the polar function, label a few points with their theta values. For example, the rightmost point of the inner loop should be labelled as theta = 0. What is theta at the leftmost point of the inner loop the first time the curve hits that point?

Try to follow the curve as theta increases from 0 to 2pi. That might give you some better insight as to what the limits of integration are. Keep in mind that you want only the area of the upper (or lower) half of the outer loop minus the area of the upper (or lower) half of the inner loop, and you will double that result.

Answer 8

ok thank you!