Chapter 5.3, Problem 14E

a.

To determine

To evaluate: The area function $A\left(2\right)$ if $A\left(x\right)={\displaystyle \underset{0}{\overset{x}{\int }}f\left(t\right)dt}$ and $F\left(x\right)={\displaystyle \underset{2}{\overset{x}{\int }}f\left(t\right)dt}$.

b.

To determine

To evaluate: The area function $F\left(5\right)$ if $A\left(x\right)={\displaystyle \underset{0}{\overset{x}{\int }}f\left(t\right)dt}$ and $F\left(x\right)={\displaystyle \underset{2}{\overset{x}{\int }}f\left(t\right)dt}$.

c.

To determine

To evaluate: The area function $A\left(0\right)$ if $A\left(x\right)={\displaystyle \underset{0}{\overset{x}{\int }}f\left(t\right)dt}$ and $F\left(x\right)={\displaystyle \underset{2}{\overset{x}{\int }}f\left(t\right)dt}$.

d.

To determine

To evaluate: The area function $F\left(8\right)$ if $A\left(x\right)={\displaystyle \underset{0}{\overset{x}{\int }}f\left(t\right)dt}$ and $F\left(x\right)={\displaystyle \underset{2}{\overset{x}{\int }}f\left(t\right)dt}$.

e.

To determine

To evaluate: The area function $A\left(8\right)$ if $A\left(x\right)={\displaystyle \underset{0}{\overset{x}{\int }}f\left(t\right)dt}$ and $F\left(x\right)={\displaystyle \underset{2}{\overset{x}{\int }}f\left(t\right)dt}$.

f.

To determine

To evaluate: The area function $A\left(5\right)$ if $A\left(x\right)={\displaystyle \underset{0}{\overset{x}{\int }}f\left(t\right)dt}$ and $F\left(x\right)={\displaystyle \underset{2}{\overset{x}{\int }}f\left(t\right)dt}$.

g.

To determine

To evaluate: The area function $F\left(2\right)$ if $A\left(x\right)={\displaystyle \underset{0}{\overset{x}{\int }}f\left(t\right)dt}$ and $F\left(x\right)={\displaystyle \underset{2}{\overset{x}{\int }}f\left(t\right)dt}$.