Hello,
How do i go about doing this question ?thanks.i appreciate the help.
Find the flux of F=x²i-xyj+3zK outwards across the surface S bounded by the planes x=0,y=0,z=0,y=1,x+z=1
The definition of "flux", which you probably know, is the sum of the integral of the flow, dot product, the (in this case) outward pointing unit normal, across each surface. For example, the outward pointing normal of the plane z= 0 is -k so the function to be integrated is $\displaystyle x^2i- xyj+3zk \cdot -k=-3z$. Of course, on the plane z= 0, that is equal to 0 so the integral is 0. The outward pointing unit normal to x+ z= 1 is i+ k so the function to be integrated is $\displaystyle x^2i- xyj+ 3zk\cdot i+ k= x^2+ 3z$. On the plane x+ z= 1, or z= 1- x that is $\displaystyle x^2+ 3(1- x)= x^2- 3x+ 3$. x runs from 0 to 1 so that will be $\displaystyle \int_0^1 x^2- 3x+ 3 dx$.