Now you'll evaluate the integral â«C6ysin(2x)dx+5xydy â« C 6 y sin â¡ ( 2 x ) d x + 5 x y d y on the closed curve C consisting of the line segments from (0,0) to (5,1) to (0,1) to (0,0) using Green's Theorem. Green's Theorem says this integral can be rewritten in the form â«â«Df(x,y)dA â« â« D f ( x , y ) d A In this integral, f(x,y) =
Setting up the double integral over the region D, you get
â«BAâ«DCf(x,y)dxdyâ«ABâ«CDf(x,y)dxdy
(Note that the order of integration is specified--for this integral it will turn out that this is the easier order of integration). In this, A =
B=
C=
D=
Evaluting this integral, â«C6ysin(2x)dx+5xydy=â«â«Df(x,y)dA=â«C6ysinâ¡(2x)dx+5xydy=â«â«Df(x,y)dA=
Now you'll evaluate the integral 6y sin(2x) dx + 5xy dy on the closed curve C consisting of the line segments from (0,0) to (5,1) to (0,1) to (0,0) using Green's Theorem. Green's Theorem says this integral can be rewritten in the form f(x,y) dA In this integral, fx.y)- Setting up the double integral over the region D, you get f(x,y) dx dy (Note that the order of integration is specified--for this integrl it will turn out that this is the easier order of integration). In this, Evaluting this integral, c6y sin(20dx + 5xydy-//D f(x, Ñ) dA-
Show transcribed image textNow you'll evaluate the integral 6y sin(2x) dx + 5xy dy on the closed curve C consisting of the line segments from (0,0) to (5,1) to (0,1) to (0,0) using Green's Theorem. Green's Theorem says this integral can be rewritten in the form f(x,y) dA In this integral, fx.y)- Setting up the double integral over the region D, you get f(x,y) dx dy (Note that the order of integration is specified--for this integrl it will turn out that this is the easier order of integration). In this, Evaluting this integral, c6y sin(20dx + 5xydy-//D f(x, Ñ) dA-
