If f(x) = 3x2 − 8x, 0 ≤ x ≤ 3, evaluate the Riemann sum with n = 6, taking the sample points to be right endpoints.

The Riemann sum of with is .

The formula for the right Riemann sum is described below:

(1)

Where:

If we know that , , and , then the Riemann sum is:

The Riemann sum of with is .

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Split up the interval [0, 3] into 6 subintervals,

[0, 1/2], [1/2, 1], [1, 3/2], [3/2, 2], [2, 5/2], [5/2, 3]

The right endpoints are given by the arithmetic sequence,

with .

We approximate the integral of on the interval [0, 3] by the Riemann sum,

Recall the formulas,

Then the value of the integral is approximately

Compare to the exact value of the integral, -9.

ad = ae + ed = y + 7

similar triangles therefor

ac/ab = ad/ae

6/4 = (y + 7) / y

cross multiply

6y = 4(y + 7)

6y = 4y + 28

2y = 28

y = 14

step-by-step explanation: