Chapter 14.5, Problem 29AYU

To determine

To find: The following for an integral $\underset{0}{\overset{2}{{\displaystyle \int }}}{e}^{x}dx$.

a. What area does the integral represent?

Answer to Problem 29AYU

a. Area under the graph of $ƒ\left(x\right)=e^x$ from 0 to 2.

Explanation of Solution

Given:

$\underset{0}{\overset{2}{{\displaystyle \int }}}{e}^{x}dx$

Calculation:

a. Area under the graph of $ƒ\left(x\right)=e^x$ from 0 to 2.

To determine

To find: The following for an integral $\underset{0}{\overset{2}{{\displaystyle \int }}}{e}^{x}dx$.

b. Provide a graph that illustrates this area.

Answer to Problem 29AYU

b.

Explanation of Solution

Given:

$\underset{0}{\overset{2}{{\displaystyle \int }}}{e}^{x}dx$

Calculation:

b. Graph:

To determine

To find: The following for an integral $\underset{0}{\overset{2}{{\displaystyle \int }}}{e}^{x}dx$.

c. Use a graphing utility to approximate this area.

Answer to Problem 29AYU

c. The area of the integral is $6.389$.

Explanation of Solution

Given:

$\underset{0}{\overset{2}{{\displaystyle \int }}}{e}^{x}dx$

Calculation:

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

That is evaluate the integral,

The value of the integral $\underset{0}{\overset{2}{{\displaystyle \int }}}{e}^{x}dx$ is $6.389$.

So, the area under the graph of $f$ from 0 to 2 is $6.389$.