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## Homework Statement

Let a>0 be a constant. Find the average value of the function f(x,y)=x^2+y^2

1) on the square -a[tex]\leq[/tex]x[tex]\leq[/tex]a, -a[tex]\leq[/tex]y[tex]\leq[/tex]a

2) on the disk x^2+y^2[tex]\leq[/tex]a^2

## Homework Equations

## The Attempt at a Solution

1) I integrated [tex]\int[/tex]a-(-a) [tex]\int[/tex]a-(-a) (x^2+y^2) dxdy and got (8/3)a^4..Is this right?

2)I converted it to polar coordinates 0[tex]\leq[/tex][tex]\theta[/tex][tex]\leq[/tex]2pi

and 0[tex]\leq[/tex]r[tex]\leq[/tex]sqrt(a)

i integrated [tex]\int[/tex]0-2pi[tex]\int[/tex]0-sqrt(a) r^2drd[tex]\theta[/tex]

and got 2/3pi*(sqrt(a)^3)... is this right???----- 2pi[tex]\frac{\sqrt{a}^3}{3}[/tex]