Let $A(x)={\displaystyle \underset{0}{\overset{x}{}}}f(t)dt$ where $f$ is the function given by the graph below.

$A(3)=$

$A^{\text{'}}(3)=$

The graph of a linear derivative function $g^{\text{'}}(x)$ is given. Find $g(x)$ if it is known that $g(-3)=-12.$

$g(x)=$

The graph of a function $y=f(x)$ is shown. Make a sketch of the antiderivative $F,$ given that $F$ is continuous and $F(0)=-3.$

The graph below shows the constant function $y=w(t).$

A new function, $f,$ is defined as an integral:

$f(x)={\displaystyle \underset{5}{\overset{x}{}}}w(t)dt$

What is the value of $f(8)?$

Answer:

We know that $f$ is an antiderivative of $w.$

What is the formula for $f?$

Answer: $f(x)=$