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Use left and right endpoints and the given number of rectangles to find two approximations of the area of the region between th...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) = 4 sin x, [0, 𝜋], 6 rectangles
left endpoints approximation Area:
right endpoints approximation Area:
g(x) = 4 sin x, [0, 𝜋], 6 rectangles
left endpoints approximation Area:
right endpoints approximation Area:
Answers
oobleck
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)
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)