Question

Find the area between the loops of the limacon =3(1 2cos).

Answer 1

To find the area between the loops of the limacon, use the formula A = r² and integrate the equation over the range of theta where the loop exists.

Step-by-step explanation:

To find the area between the loops of the limacon, we can use the formula A = r², where r is the distance from the origin to any point on the loop. Given that the limacon equation is r = 3(1 + 2cos(theta)), we can substitute this into the formula to get A = (3(1 + 2cos(theta)))². To find the area, we need to integrate this equation over the range of theta where the loop exists.