Iterated Integrals: Examples

1. Evaluate the following funciton: 2*x^2*y^-2+2*y first with y=1..x, next with x=1..2

Anwser:

This can be done in one step with the int command nested inside of another int command:

>	int(int(2*x^2*y^(-2)+2*y,y=1..x),x=1..2);

2. Using Iterated Integrals, prove that the area of a rectangle is one side multiplied by the other.

Anwser:

Set up an integrol with the f(x,y)=1 over the region x=a..b and y=c..d:

>	int(int(1,y=c..d),x=a..b);

>	factor(%);