Eat green vegetables. They are healthy

As I said eat green vegetables. Oh and also use Green's Theorem in plane. $\oint _{ c }^{ }{ Mdx+Ndy=\iint _{ R }^{ }{ [∂N/∂x- } { ∂M/∂y]dxdy } }$

Where R is the region bounded by the closed curve "c" and M, N are functions of x and y Hence, for given problem, $∂N/∂x-∂M/∂y=x$ So given integral becomes, $\iint _{ R }^{ }{ xdxdy=\int _{ r=0 }^{ 1 }{ \int _{ \theta =0 }^{ 2π }{ cos\theta rdrd\theta =0 } } }$

When we calculate...then u will find that there is not any kind of roll of this function inside the circle .....so then apply gauss law that net flux should be zero....

Replace x with cos(theta) and y for sin(theta) now integral over whole circle's point means theta changing from 0 to 2pi now substituting these values to obtain limits of x,y which corresponds to 0. now, since both upper limit and lower limit coincides therefore integral resolves to 0.