Area of the hypotrochoide
Problem 9
Find the total area bounded by hypotrochoide given by parametric equations:
$$ x(t) = (a+b)\cos(t) + b\cos\left(\frac{a+b}{b}t\right) $$
$$ y(t) = (a+b)\sin(t) + b\sin\left(\frac{a+b}{b}t\right) $$
for the values of the parameters $a=1$ and $b=-\frac{11}{7}$.