# Green's Theorem Enclosed Curves

Use Green's Thereom to find the area enclosed by the curve:

{abs(x)}^(1/2) + {abs(y)}^(1/2) = 1.

It is important that you solve this problem using Green's Method because that is how my professor prefers it.

I know that you have to make the above statement true and switch to a different set of coordinates. Something along the lines of x = cos raised to the fourth power as well as y = sin raised to the fourth power to make the above statement true.

I believe the final answer is 2/3.

Edit - When you graph this equation, it appears as a diamond with all four sides caved in so to speak.

So, I know we have to find the area simply of the graph in the first quadrant and then times that area by four. Hope that helps.

Further, using Green's Thereom we must choose P and Q values. Since integrating over 1 will find us any area, we simply make dQ 1 and dP 0 so when we subtract the two we are left with 1. That's all I recall from my professor's lecture.

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Use Green's Thereom to find the area enclosed by the curve:

{abs(x)}^(1/2) + {abs(y)}^(1/2) = 1.

It is important that you solve this problem using Green's Method because that is how my professor prefers it.

I know that you have to make the above statement true and switch to a different set of coordinates. Something along the lines of x = cos raised to the fourth power as well as ...

#### Solution Summary

The expert uses Green's Theorem to find the area enclosed by the curves. Functions are analyzed.