Find the Riemann sum for f(x) = 3 sin x, 0 ≤ x ≤ 3π/2, with six terms, taking the sample points to be right endpoints. (a) Find the Riemann sum for f(x) = 3 sin x, 0 ≤ x ≤ 3π/2, with six terms, taking the sample points to be right endpoints. (Round your answers to six decimal places.) R6=____________ (b) Repeat part (a) with midpoints as the sample points. M6=____________

Expert Answers

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You need to find the width of interval, hence you may use the formula:

`Delta x = (3pi/2 - 0)/6 =gt Delta x = 3pi/12 =gt Delta x = pi/4`

You need to find the 6 right endpoints such that:

x_1 = pi/4 ; x_2 = pi/4 + pi/4 = pi/2

`x_3 = pi/2 + pi/4 = 3pi/4`

`x_4 = 3pi/4 + pi/4 = pi`

`x_5 = pi+pi/4 = 5pi/4`

`x_6 = 5pi/4 + pi/4 = 6pi/4 =gt x_6 = 3pi/2` 

You need to remember the formula of Riemann's sum such that:

`R_6 = sum_(i=1)^6 f(x_i)Delta x`

`R_6 =...

(The entire section contains 216 words.)

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