The height of each trapezoid is found by taking the difference between the endpoints anddividing by n. Here, the width of each trapezoid is = .We find the bases of the trapezoids by evaluating y = 2x − x^2 at the appropriate endpoints.y(1) = 2(1) − (1)^2 = 1; = ; = ; = ; and y(2) = 2(2) − (2)^2 = 0.Therefore, the area is = = .4.
First, let’s draw a picture.