Math 234-Calculus II Summer 2020

Lab 1

1 Directions

The labs for Calculus II will follow the same format as the labs for Calculus I from last semester. That is you will need to go to https://student.desmos.com and type in this lab's code: 8JN DZT. After that, pages will be given you to answer the following questions. If you are unfamiliar with desmos or this lab format, I suggest you look at the Calculus I labs and their solutions from last semester; this will give you an idea of how to format your solutions. The labs save automatically, and will be collect on or after the due date. Once they are collected, they can't be changed.

The graph \(0\leq y \leq f(x)\) for an unknown function \(f(x)\) is given to you. Complete the following problems.

1.1 Problem 0

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

1.2 Problem 1

Let \(F(x)\) be the area under the graph of \(f(x)\) and above the \(x\)-axis over \([a,x]\) for \(x \in [a,b]\). Define and graph \(F(x)\) in blue.

1.3 Problem 2

Find the (approximate) area under the graph of \(f(x)\) and above the \(x\)-axis over \([0,4]\).

1.4 Problem 3

What is the slope of the line tangent to the graph of \(F(x)\) at \(x=2\)?

1.5 Problem 4