Q. 3 - Calculus

Question

Use a definite integral to express the function whose output

at any real number x is the signed area between the

graph of $f\left(t\right)=t^2$ and the $t-axis$ on $\left[2, x\right]$.

Step-by-Step Solution

Answer

The definite integral is ${\int }_2^x{t}^{2}dt$

Step 1. To find

A definite integral whose output at any real number is the signed area between the graph of and the -axis on [2,x]. 

Step 2. Calculation

The definite integral is ${\int }_2^x{t}^{2}dt$