Chapter 14, Problem 16CT

To determine

The integral that represents the following shaded area. Do not evaluate it.

Answer to Problem 16CT

Solution:

The integral which represents the shaded area is ${\displaystyle {\int }_1^4\left(-x^2+5x+3\right)dx}$.

Explanation of Solution

Given information:

The graph:

Explanation:

By observing the graph the shaded region is under the graph of function $f\left(x\right)=-x^2+5x+3$ and it is from $x=1$ to $x=4$.

So the area of shaded region is represented by the integral from $1$ to $4$ of $f\left(x\right)$ that can be written as ${\displaystyle {\int }_1^4\left(-x^2+5x+3\right)dx}$.

Hence, the integral which represents the shaded area is ${\displaystyle {\int }_1^4\left(-x^2+5x+3\right)dx}$.