Use left and right endpoints and the given number of rectangles to find two approximations of the area of the region between the graph of the function and the x-axis over the given interval. (Round your answers to four decimal places.)

Question

g(x) = 4 sin x, [0, 𝜋], 6 rectangles
left endpoints approximation Area:
right endpoints approximation Area:

Answer 1

the left endpoints are at x = 0, 𝜋/6, ... 5𝜋/6
so the area is
4*𝜋/6 (f(0) + f(𝜋/6) + ... + f(5𝜋/6)) = 4*𝜋/6 (0 + 1/2 + √3/2 + 1 + √3/2 + 1/2) = 4*𝜋/6 (2+√3)
the right endpoints are the same, since f(𝜋) = f(0)