Q. 12 - Calculus

Question

Consider the following graph A(x)=$A\left(x\right)={\int }_0^{x}f\left(t\right)dt$

List the quantities A(1),A(3), A(6),A(7)

Step-by-Step Solution

Answer

The order is A(1) <A(6)<A(3)<A(7).

Step 1. Graph of the signed area from x=0 to x=1

The given function$A\left(x\right)={\int }_0^{x}f\left(t\right)dt$

Step 2. Graph of the signed area from x=0 to x=1

Step 3. Graph of the signed area from x=0 to x=3

Step 4. Graph of the signed area from x=0 to x=6

Step 5. Graph of the signed area from x=0 to x=7

Step 6. Result

Clearly we can see that A(1) <A(6)<A(3)<A(7).