Chapter 14.5, Problem 24AYU

To determine

To find: The following for an integral $\underset{1}{\overset{3}{{\displaystyle \int }}}\left(-2x+7\right)dx$.

a. What area does the integral represent?

Answer to Problem 24AYU

a. Area under the graph of $ƒ\left(x\right)=-2x+7$ from 1 to 3.

Explanation of Solution

Given:

$\underset{1}{\overset{3}{{\displaystyle \int }}}\left(-2x+7\right)dx$

Calculation:

a. Area under the graph of $ƒ\left(x\right)=-2x+7$ from 1 to 3.

To determine

To find: The following for an integral $\underset{1}{\overset{3}{{\displaystyle \int }}}\left(-2x+7\right)dx$.

b. Provide a graph that illustrates this area.

Answer to Problem 24AYU

b.

Explanation of Solution

Given:

$\underset{1}{\overset{3}{{\displaystyle \int }}}\left(-2x+7\right)dx$

Calculation:

b. Graph:

To determine

To find: The following for an integral $\underset{1}{\overset{3}{{\displaystyle \int }}}\left(-2x+7\right)dx$.

c. Use a graphing utility to approximate this area.

Answer to Problem 24AYU

c. The area of the integral is 6.

Explanation of Solution

Given:

$\underset{1}{\overset{3}{{\displaystyle \int }}}\left(-2x+7\right)dx$

Calculation:

c. Use a graphing utility to approximate the area of the integral.

That is evaluate the integral,

The value of the integral $\underset{1}{\overset{3}{{\displaystyle \int }}}\left(-2x+7\right)dx$ is 6.

so the area under the graph of $f$ from 1 to 3 is 6.