Question

Write the integral that represents the shaded area. Do not attempt to evaluate

Short answer

The required integral is${\int }_1^4\left(-x^2+5x+3\right)dx$

Step-by-step solution

Step 1. Given  information

We are given a graph of a function$f\left(x\right)=-x^2+5x+3$

We need to find the integral that represents its area.

Step 2. Integral Value Of Area

It is clear from the graph that the given function is $f\left(x\right)=-x^2+5x+3$

and the boundaries are$a=1\text{and}b=4$

Also, we know,

${\int }_a^{b}f\left(x\right)dx$

Therefore, the required integral is

${\int }_1^4\left(-x^2+5x+3\right)dx$