section 14: ftoc & antidifferentiation score: 9/11 answered: 6/8 question 7 suppose f(2)=2, f(5)= - 3, and…

section 14: ftoc & antidifferentiation score: 9/11 answered: 6/8 question 7 suppose f(2)=2, f(5)= - 3, and f(x)=f(x). ∫₂⁵f(x)dx= question help: video written example

section 14: ftoc & antidifferentiation score: 9/11 answered: 6/8 question 7 suppose f(2)=2, f(5)= - 3, and f(x)=f(x). ∫₂⁵f(x)dx= question help: video written example

Answer

Explanation:

Step1: Recall the Fundamental Theorem of Calculus (FTOC)

If $F'(x)=f(x)$, then $\int_{a}^{b}f(x)dx = F(b)-F(a)$.

Step2: Identify the values of $a$, $b$, $F(a)$ and $F(b)$

Here, $a = 2$, $b = 5$, $F(2)=2$ and $F(5)= - 3$.

Step3: Calculate the definite - integral

$\int_{2}^{5}f(x)dx=F(5)-F(2)$. Substitute the values: $F(5)-F(2)=-3 - 2=-5$.

Answer:

$-5$