Find the area under one arch of the trochoid of Exercise 40 in Section 10.1 for the case d < r.
In Exercise 40 Let P be a point at a distance from the center of a circle of radius r. The curve traced out by P as the circle rolls along a straight line is called a trochoid. (Think of the motion of a point on a spoke of a bicycle wheel.) The cycloid is the special case of a trochoid with d = r. Using the same parameter θ as for the cycloid and, assuming the line is the -axis and θ = 0 when P is at one of its lowest points, show that parametric equations of the trochoid are
x = rθ - d sinθ y = r - d cos θ
Sketch the trochoid for the cases d < r and d > r.