Question

Check it:

Find average value of function f(x,y)=x^2+y^2 over the square region [0,a]x[0,a] where a>0

Answer 1

i did :\[\int\limits_{0}^{a}\int\limits_{0}^{a}x^2+y^2dxdy\]

Answer 2

i got a^4/3 +a^4/3

Answer 3

The integral is correct, but that gives the SUM of (x^2 + y^2) over the area.

Answer 4

then i did \[\int\limits_{0}^{a}\int\limits_{0}^{a}dxdy\]

Answer 5

Ah, yes =) You're getting there.

Answer 6

that gave me a^2

Answer 7

Right. It's a square with sidelength a. So area is a^2

Answer 8

so then divided both integrals

Answer 9

and i got: 2/3(a^2)

Answer 10

That matches my answer.