Use the Midpoint Rule with n = 5 to approximate the integral.

Question

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int_0^10 (3 sin(sqrt(q))) d q

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Round your answer to three decimal places.

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a.
25.146

b.
24.346

c.
23.846

d.
18.846

e.
23.346

Answer 1

To use the Midpoint Rule with n = 5, we first divide the interval [0, 10] into 5 subintervals of equal width:

Δx = (10-0)/5 = 2

The midpoints of these subintervals are: 1, 3, 5, 7, and 9.

Now, we plug these midpoints into the function 3sin(√x) and sum the results:

3sin(√1) + 3sin(√3) + 3sin(√5) + 3sin(√7) + 3sin(√9)

≈ 3(0.841) + 3(0.614) + 3(-0.959) + 3(-0.426) + 3(0)

≈ 2.523 + 1.842 - 2.877 - 1.278

≈ 0.210

Finally, we multiply this sum by Δx to get the approximate value of the integral:

0.210 * 2 = 0.420

Therefore, the integral of 3sin(√q) from 0 to 10 using the Midpoint Rule with n = 5 is approximately 0.420.

Rounded to three decimal places, the answer is 0.420, which is not provided in the answer choices.