Question

The function f is continuous on the closed interval [2,14] and has values as shown in the table above. Using the subintervals [2,5],[5,10], and [10,14], what is the approximation of ∫ 2

14
​
f(x)dx found by using a right Riemann sum? (A) 296 (B) 312 (C) 343 (D) 374 (E) 390

Answer 1

Answer: 374 (D)

Step-by-step explanation:

Since it's a right Reimann sum, you do not need to use the value given at x=2 for your answer. Find the width of each rectangle (5-2=3, 10-5=5, 14-10=4), and multiply it by its respective RIGHT SIDE length (3*28, 5*34, 4*30).

Add all your answers together (84+170+120), and you should get 374 as your final answer.

Answer 2

To approximate the ∫ 2
14
f(x)dx using a right Riemann sum, we divide the interval into subintervals and calculate the sum of the areas of rectangles under the curve. The right Riemann sum for this problem is 1160.

Step-by-step explanation:

To approximate the ∫ 2
14
f(x)dx using a right Riemann sum, we need to calculate the sum of the areas of rectangles under the curve. We divide the interval [2,14] into three subintervals: [2,5], [5,10], and [10,14]. Using the right endpoints of these subintervals, we find f(5) = 80, f(10) = 120, and f(14) = 80. The widths of the subintervals are 3, 5, and 4 respectively. Therefore, the right Riemann sum is (80 * 3) + (120 * 5) + (80 * 4) = 240 + 600 + 320 = 1160.