Question

Green's Theorem

Answer 1

i'm really struggling with this new material :(

Answer 2

uSE THIS
huge\\[\int\limits_{deltaD}^{?}f(x,y)dx+g(x,y)dy \int\limits_{?}^{?}\int\limits_{D}^{?}dxdy\]

Answer 3

erm

Answer 4

it's the d integral of 3 right? how do you know what the limits of integration are though

Answer 5

just find them from setting them equal to each other?
so x is 0 < x < 3
then y is um

Answer 6

hrm

does that sound right?

Answer 7

y is
lower = x^2-2x
upper = x

Answer 8

erm i'm lost on this

Answer 9

now we need to find where will y=x and the parabola intesect so that we can set the bounds for our x. so we'll have
y=x^2-2x
x=x^2-2x
x^2-3x=0
x=0 and intersection also at x=3
so at this iinterval, the graph will look like this:

Answer 10

so the bounds will be
0<=x<=3
x^2-2x<=y<=x.
now we'll get:
\[\int\limits_{0}^{3} \int\limits_{x^2-2x}^{x}9dydx\]

Answer 11

can you evaluate this integral? or should I continue?

Answer 12

I got the 9 from getting the curl F=9