Question

The difference between the greatest and least values of the function $F\left(x\right)={\int }_0^x(t+1)dt$ on $[2,3]$ is

• A. $3$
• B. $2$
• C. $7/2$
• D. $11/2$

Answer 1

The correct option is C $7/2$

$F\left(x\right)={\int }_0^x(t+1)dt\Rightarrow F^{\prime }\left(x\right)=x+1>0x\in [2,3]$
So the difference of greatest and least value is
$F\left(3\right)-F\left(2\right)={\int }_2^3(t+1)dt=\frac{7}{2}$