Question

9 mark for review the graph of the function f shown above consists of three line segments. if h is the function defined by $h(x)=int_{0}^{x}f(t)dt$ for $0leq xleq5$, then $h(3)$ is a 0 b 4 c 10 d undefined

Explanation:

Step1: Recall fundamental theorem of calculus

If $h(x)=\int_{0}^{x}f(t)dt$, then $h'(x) = f(x)$ by the fundamental theorem of calculus.

Step2: Evaluate $h'(3)$

Since $h'(x)=f(x)$, then $h'(3)=f(3)$.

Step3: Find $f(3)$ from the graph

Looking at the graph of $y = f(x)$, when $x = 3$, the value of the function $f(x)$ is $4$.

Answer:

B. 4