area of the region inside this ellipse. [ Hint: Write half the area as an integral and then change variables in the integral so that it becomes the integral for the area inside a semicircle.] 34. The curve x2/a2 + y2/b2 = 1, where a and b are positive, describes an ellipse (Fig. 7.3.1). Find the (0,b) (a, 0) (-a, 0) (0, -b) Figure 7.3.1. Find the area inside the ellipse