Calculus Help Please Urgent!!!

Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to four decimal places.

integral from o to pi/2 (2cos^3(x))dx ,
n = 4

M4 = ??????

Thanks!!!

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  1. With 4 divisions, the boundaries are
    0 pi/8 pi/4 3pi/8 pi/2
    So, the midpoints are at
    pi/16,3pi/16,5pi/16,7pi/16

    So, we have 4 rectangles with width dx=pi/8, and heights
    2cos^3(pi/16),...

    Add up the areas of the rectangles. I get 1.3330

    To check,

    ∫[0,pi/2] 2cos^3(x) dx = 4/3 = 1.3333

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