Math 234-Calculus II Summer 2020

Lab 3

1 Directions

Go to https://student.desmos.com and type in this lab's code: UPM 6BQ.

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

1.1 Problem 0

Enter your name and SFA email, I need to know who to give the grades to.

1.2 Problem 1

Add sliders for \(N \in [2,3,\ldots, 100]\), \(a,b \in [-10,10]\).
Approximate the area under the curve of \(f(x)\) over \([a,b]\) with \(N\) partitions using the Midpoint Rule. Your answer should reflect changes in any of the three sliders defined in Step 1.

1.3 Problem 2

Approximate the area under the curve of \(f(x)\) over \([a,b]\) with \(N\) partitions using the Trapezoid Rule. Your answer should reflect changes in any of the three sliders defined in Problem 1.

1.4 Problem 3

Do this problem last, as it may slow down your computer. Define and graph the function function \[E(x) = \int_0^x f(t)\, dt.\] The function \(E\) is called the Error Function and is frequently used.