Question

In Problems 43 and 44, an integral is given.

(a) What area does the integral represent?

(b) Provide a graph that illustrates this area.

(c) Use a graphing utility to approximate this area.

${\int }_{-1}^1{e}^{x}dx$

Short answer

a) The integral represents the area under the curve between$-1,1$

b) The area under the curve is shaded.

c) The area is$2.35$

Step-by-step solution

Part (a) Step 1. Explaining the integral

Given integral is${\int }_{-1}^1{e}^{x}dx$.

The integral represents the area under the curve $f\left(x\right)=e^x$between the limits $-1,1$.

Part(b) Step 1. Graph representing the area

Graph the function $f\left(x\right)=e^x$and shade the area between the limits $-1,1$.

Part(c) Step 1. Area using a graphing utility

On a graphing utility first, enter the function $f\left(x\right)=e^x$.

Next to find the area give the function as 9:fnlnt(, VARS, Y-VARS, 1:Function, 1:Y1,X,-1,3)

The calculator will give the area as $2.35$.