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 \(x^{\frac{2}{3}} + y^{\frac{2}{3}}=4\)?

The graph above satisfy the equation \(x^4 + y^3 = x^2 y \).

The 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 \(a+b\)?

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