For a National Board Exam:
Find the area which is inside the curve r=3cos(theta) and outside the
cardoid r=1+cos(theta)
Answer is pi
Ok I am trying to setup the right definite integral for the calculator, I've tried:
Using the formula for finding area of polar curves:
$${ A = \int^b_a \frac{1}{2} f(\theta)^2 d\theta}$$
$${ A = \int^{2\pi}_0 \frac{1}{2} ( 3cos(\theta) – (1+cos(\theta)))^2 d\theta = 3\pi}$$
What is the right integral?
Best Answer
HINT...You need to establish where the curves intersect in order to determine the limits, so solve $3\cos \theta=1+\cos \theta$.
So your limits are $\pm\frac {\pi}{3}$