Question

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Question 10(Multiple Choice Worth 10 points)
(06.03 MC)
Which integral can be approximated by a right Riemann sum where f(x) = 2x³ +3 on the interval [2, 6]?

Answer 1

The definite integral of a function f(x) over an interval [a, b] can be approximated by a right Riemann sum as follows:

∫_a^b f(x) dx ≈ (b - a) * [f(a) + f(b) ] / 2

In this case, the function f(x) = 2x^3 + 3, the interval is [2, 6], and the right Riemann sum is calculated as follows:

∫_2^6 (2x^3 + 3) dx ≈ (6 - 2) * [ (2 * 2^3 + 3) + (2 * 6^3 + 3) ] / 2
= 4 * [ (2 * 8 + 3) + (2 * 216 + 3) ] / 2
= 4 * [ 19 + 459 ] / 2
= 4 * 438 / 2
= 876

So, the right Riemann sum for the definite integral of f(x) = 2x^3 + 3 on the interval [2, 6] is approximately 876.