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...

LetP be a point at a distanced from the center of a circle of radiusr. The curve traced out byP as the circle rolls along a straight line is called atrochoid. (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 thex-axis and θ = 0 whenP 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 <>