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) = 7 sin x, [0, π], 6 rectangles
left endpoints approximation Area:
right endpoints approximation Area:

Answer 1

clearly the rectangles are bounded at

x = 0, π/6, π/3, π/2, 2π/3, 5π/6, π

So, evaluate g(x) at the boundaries and add up the areas. What do you get?

There are plenty of online calculators for this to check your work.

Answer 2

3.73

Answer 3

g(x) = 7 sin x, [0, π], 6 rectangles

left endpoints approximation Area: 13.6787
right endpoints approximation Area: 13.6787

Answer 4

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) = 4 sin x, [0, π], 6 rectangles