Question

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.)

g(x) = 3 sin(x), [0, 𝜋], 6 rectangles

Answer 1

assuming equal intervals, each is of width π/6, so the Left-Endpoint approximation is

∑ f(kπ/6) ∆x
k=0..5
= 3*π/6 (f(0) + f(π/6) + ... + f(5π/6))
= π/2 (0 + 1/2 + √3/2 + 1 + √3/2 + 1/2)
= π (1+√3)