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 $\left[2,x\right]$.

Short answer

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

Step-by-step solution

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${\int }_2^x{t}^{2}dt$