overall accuracy: 86.2% record: 21 score: 21 select value of the twice differentiable function f and its…

overall accuracy: 86.2% record: 21 score: 21 select value of the twice differentiable function f and its derivative are shown in the table below. what is the value of the expression ∫₁³f″(x)dx? x 0 1 3 6 f(x) 2 5 13 16 f′(x) 4 6 0 5 -3 8 4 -6

overall accuracy: 86.2% record: 21 score: 21 select value of the twice differentiable function f and its derivative are shown in the table below. what is the value of the expression ∫₁³f″(x)dx? x 0 1 3 6 f(x) 2 5 13 16 f′(x) 4 6 0 5 -3 8 4 -6

Answer

Explanation:

Step1: Apply fundamental theorem of calculus

By the fundamental theorem of calculus, if (F'(x)=f(x)), then (\int_{a}^{b}f(x)dx = F(b)-F(a)). For (\int_{1}^{3}f''(x)dx), we know that if (F'(x)=f'(x)), then (\int_{1}^{3}f''(x)dx=f'(3)-f'(1)).

Step2: Find values from the table

From the table, (f'(1) = 6) and (f'(3)=0).

Step3: Calculate the result

(f'(3)-f'(1)=0 - 6=-6)

Answer:

(-6)