Volume of the n-dimensional ball

Please refer to the lab handout and the class lecture for the details. This is the Wolfram Cloud version of the notebook. Use the desktop version if it is available to you; the typesetting is a bit more human-friendly.

Computing definite integrals using Wolfram Cloud

Follow the syntax of the following cell to compute the definite integral of sin(x) between 0 and the square root of 17. Make sure to follow the capitalization and parentheses conventions. You will get entertaining errors if you do not!
In[]:=
Integrate[Sin[x],{x,0,Sqrt[17]}]
For iterated integrals, you just have to add the range for the other variables. The order is a little tricky. The last variable is integrated first. In the example below, integration is first with respect to x and then with respect to y:
In[]:=
Integrate[x^2+y^2,{y,0,1},{x,-1,y}]
The following example will compute the area of a circle of radius 1. Use it as inspiration for the rest of the lab:
In[]:=
Integrate[1,{y,-1,1},{x,-Sqrt[1-y^2],Sqrt[1-y^2]}]

Plotting sequences using Wolfram Cloud

The following command will plot a list of numbers. If you want fancy things like labels, look in the Mathematica documentation. It may be useful for your homework:
In[]:=
ListPlot[{1.1,1.9,2.3,0.7,9.2}]
Out[]=
1
2
3
4
5
2
4
6
8