Question

The function f is continuous son the interval [2, 10] with some of its values given in the table below. Use a right Riemann Sum approximation with 4 rectangles to approximate the integral from 2 to 10 of f of x dx.
x 2 4 7 9 10
f(x) 0 3 8 15 18

answer choices:
30.5
78.0
40.0
59.0

Answer 1

The 4 subintervals are given: [2, 4], [4, 7], [7, 9], and [9, 10].

Each subinterval has length: 4 - 2 = 2, 7 - 4 = 3, 9 - 7 = 2, and 10 - 9 = 1.

Over each subinterval, we take the value of the function at the right endpoint: 3, 8, 15, and 18.

Then the integral is approximately

$\displaystyle\int_2^{10}f(x)\,\mathrm dx\approx3\cdot2+8\cdot3+15\cdot2+18\cdot1=78$

so 78.0 is the correct answer.

Answer 2

Answer:

LammettHashAce

The 4 subintervals are given: [2, 4], [4, 7], [7, 9], and [9, 10].

Each subinterval has length: 4 - 2 = 2, 7 - 4 = 3, 9 - 7 = 2, and 10 - 9 = 1.

Over each subinterval, we take the value of the function at the right endpoint: 3, 8, 15, and 18.

Then the integral is approximately

so 78.0 is the correct answer.

Step-by-step explanation: