Question

(a) Estimate the area under the graph of f(x) = 2 cos(x) from x = 0 to x = π/2 using four approximating rectangles and right endpoints. (Round your answers to four decimal places.)
(b) Repeat part (a) using left endpoints

Answer 1

So for a problem like this, you simply want to use the x-interval to act as the width of a rectangle and then, for part a, use the right endpoint's y-value to substitute into your function.

For the first rectangle, considering you are going from x=0 to x=pi/2, it would be best to use intervals of pi/8.

So the first interval is x=0 to pi/8, which is a rectangle width of pi/8, or 0.3927. Now you want to find the y-value, or the rectangle height, at pi/8 which is the right endpoint.

f(pi/8)=2cos(pi/8) = 2(0.9329) = 1.8478

Area of rectangle = width x height = (0.3927) x (1.8478) = 0.7256

So 0.7256 would be the area of your first rectangle. Simply go through this method for the next three. You will notice that your area will change slightly for each rectangle. At the end, simply sum all four rectangles to get the approximate area.

Answer 2

ok thank you