Calculus
# Calculus of Parametric Equations

The parametric equation of a cycloid is given below.

$\large x = a(t - \sin t) \\ \large y = a(1 - \cos t)$

What is the area of the region bounded by the two arcs of the cycloid in the above figure?

What is the length of the arc of the curve $x^{\frac{2}{3}} + y^{\frac{2}{3}}=4$?

$x^4 + y^3 = x^2 y$.

The graph above satisfy the equationThe area enclosed by the 2 *cute adorable little fine* loops is equals to $\frac {a}{b}$ for coprime positive integers $a$ and $b$. What is the value of $a+b$?