Let P be a point at a distance d 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 x-axis and θ = 0 when P is at one of its lowest points, parametric equations of the trochoid are x = rθ − d sin(θ)    y = r − d cos(θ). Find the area under one arch of the trochoid found above for the case d < r.

Let P be a point at a distance d 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 x-axis and θ = 0 when P is at one of its lowest points, parametric equations of the trochoid are

Find the area under one arch of the trochoid found above for the case d < r.