Double Integrals {cal3 exm2}

https://tutorial.math.lamar.edu/Solutions/CalcIII/IteratedIntegrals/Prob1.aspx

2 examples:

• A = disk, $\partial A$=Circle
• A = Filled rectangle, $\partial A$=Outline rectangle

ex1)

Write y=x as a level cruve of some $f(x,y)$

• f(x,y)=x-y, f(x,y)=0!

ex2)

Let A = [1,2] x [0,1]

1. Plot A?

• Some filled in rectangle with given cords

1. What is $\int {\int }_R{x}^2+ydA$ (where A = area)

• ${\int }_0^1{\int }_1^2{x}^2+ydxdy$
• Read this $\int$ as a stack (FIFO), so look @ inner integral first (2→1)

Q1) Let R = [-1,1] $\times$ [0,3]

• plot R
• $\int {\int }_R{x}^{3}y-xdA$
• Answer =0!