Question

Your calculator should be able to approximate the area between a graph and the x-axis. Determine how to do this on your particular calculator, and then, in Exercise, use the method to approximate the signed area between the graph of each function f and the x-axis on the given interval [a, b].

$f\left(x\right)=e^x,\left[a,b\right]=\left[1,4\right]$

Short answer

Answer is 51.88

Step-by-step solution

Step 1. Given information

Function is$f\left(x\right)=e^x,\left[a,b\right]=\left[1,4\right]$

Step 2. Explanation

Consider the function $f\left(x\right)=e^x$

Area $={\int }_1^4{e}^x$

$$\begin{gathered} =e^4-e \\ =51.88 \end{gathered}$$