Q. 13 - Calculus

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:

Step-by-Step Solution

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 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,

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