Question

Evaluate the double integral of (y-2x^2)dA over R where R is the region bounded by the square |x|+|y|=1.

Answer 1

Your square is the picture in the attached file
It is bounded by the four lines
\[(y=1-x,y=-x-1,y=x+1,y=x-1)
\]
It should be easy now to set up the integral.

Answer 2

Your in integral will be
\[
\int _{-1}^0\int
_{-x-1}^{x+1}\left(y-x^2\right)dydx+\int _0^1\int
_{x-1}^{1-x}\left(y-x^2\right)dydx
\]
compute these two integrals, you will find them equals. Could you have predicted that?

Answer 3

I have 4 partitions :))

Answer 4

Only two.

Answer 5

Do I have to expand all these?

Answer 6

No, you do integrate first with respect to y, then with respect to x

Answer 7

I got 2(1/2 -2/3)

Answer 8

-1/3

Answer 9

That is right.

Answer 10

YAAAAAAY! Thanks! You're a genius! :)

Answer 11

yw