Calculus I

Lab 10

Directions

Go to https://student.desmos.com/ and enter the code CDW45R. Your work saves automatically. You may use your book and notes, and this lab may require some scratch work. Complete the following (there are corresponding slides for each problem):

Problem 0

Enter in your name, I need to know who to give the grades to.

Problem 1

Let \(\displaystyle f(x) = \frac{1}{\sqrt{\pi}} e^{-x^2}\).

Graph \(f(x)\).
Set \(a=-3, b=3\), and make a slider for \(N \in \{2,3,\ldots 100\}\).
Have Desmos calculate \(M_N\) for whatever \(N\) the slider is on. See page 268 in your textbook, and this example may be helpful as well (be sure you understand the example).
Graph the rectangles used in calculating \(M_N\).
Find the estimate of Desmos for \(\displaystyle \displaystyle \int_a^b f(x)\, dx\).
Make an estimate of \(\displaystyle \int_{-\infty} ^\infty f(x)\, dx\).