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Problem:

##\int_R (x-y)dx \ dy=-2/3 ## for ##R=\{(x,y):x^2+y^2 \geq 1; y \geq 0\}## by

a.) Direction integration,

b.) Green's theorem.

Attempt at a Solution:

I'm a little confused with part a. Wouldn't the region R be defined by all the points above the y-axis that lie on, in addition to above, the circle of radius 1 centered at the origin?

I'm confused on what the limits of integration would be for the integral ##\iint (x-y) dx \ dy##.

##\int_R (x-y)dx \ dy=-2/3 ## for ##R=\{(x,y):x^2+y^2 \geq 1; y \geq 0\}## by

a.) Direction integration,

b.) Green's theorem.

Attempt at a Solution:

I'm a little confused with part a. Wouldn't the region R be defined by all the points above the y-axis that lie on, in addition to above, the circle of radius 1 centered at the origin?

I'm confused on what the limits of integration would be for the integral ##\iint (x-y) dx \ dy##.

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