let $g(x)=int_{0}^{x}f(t)dt$, where $f$ is the function whose graph is shown below. what is the value of…

let $g(x)=int_{0}^{x}f(t)dt$, where $f$ is the function whose graph is shown below. what is the value of $g(3)$?

let $g(x)=int_{0}^{x}f(t)dt$, where $f$ is the function whose graph is shown below. what is the value of $g(3)$?

Answer

Explanation:

Step1: Apply the Fundamental Theorem of Calculus Part 1.

The Fundamental Theorem of Calculus Part 1 states that if $g(x) = \int_{a}^{x} f(t) dt$, then $g'(x) = f(x)$. Given $g(x) = \int_{0}^{x} f(t) dt$. Thus, $g'(x) = f(x)$.

Step2: Evaluate $g'(3)$.

To find $g'(3)$, we need