Chapter 5.1, Problem 13E

To determine

To find: The area of the region.

Answer to Problem 13E

The area is $0.88208$ .

Explanation of Solution

Given information:

The equation is:

  $\begin{array}{c}f(x)=e^{-x^2},\\ a=0,\\ b=2\end{array}$

Calculation:

To remedy this issue, a RAM calculator program. For information on how to obtain one if don't already have one, please refer to solution for the earlier exercise where fill in the table with the values of $LRA{M}_n$ , $MRA{M}_n$ and $RRA{M}_n$ for $n=10,50,100,500$ to how to get one.

Calculate Riemann sums repeatedly for bigger and bigger values of $n$ until  detect value the Riemann sum is approaching to estimate the region's size. Although LRAM or RRAM are also options, to use MRAM. The values of $n$ that selected to use are the same as those in the table from the preceding exercise because they are adequate to estimate the area. $n$ use alternative values, but in order to obtain an accurate estimate, must use big values of $n$ .

The given equation is $f(x)=e^{-x^2}$ hence, enter this under $Y_1$ , $a=0$ is the provided lower bound. So, when the software asks for "A", "LEFTEND", or any term that denotes lower bound, enter this. When the program asks for B, RIGHTEND, or another word that signifies upper bound, enter this value: $b=2$

To use the program than gives the following values:

$n$	$MRA{M}_n$
10	0.882202
50	0.882086
100	0.882083
500	0.882081

From the table, the area is than approaching $0.88208$ .

Therefore the required area is $0.88208$ .