Question

Let $f$be the function graphed in Exercise$12$, and define $A\left(x\right)={\int }_0^{x}f\left(t\right)dt$List the following quantities in order from smallest to largest:

Short answer

The quantities in order from the smallest to the largest is,

$A\left(5\right)<A\left(0\right)<A(-1)<A(-2)$.

Step-by-step solution

Step 1. Given information

The given graph in Exercise $12$is,

Step 2. The signed area from x=0 to x=-1 is shown below in shade:

Step 3. The signed area from x=0 to x=-2 is shown below in shade.

Step 4. The signed area from x=0 to x=5 is shown below in shade.

Clearly, from the above figures it is clear that,

$A\left(5\right)<A\left(0\right)<A(-1)<A(-2)$.