Question

Verify Stoke's theorem for F = x2i+ xyj where S is the square
in the plane z=0 and whose sides are along the lines x=0,
y=0, x=a, y=a.​

Answer 1

Answer:

Given $F\:=\:x^2i+xyj$

For this Stoke's theorem says:

$\int \:F.dr\:=\int \int \left(\nabla X\:F\right).n\ ds$

L.H.S = $\int \:F.dr\:$ = $\frac{a^{3} }{2}$

R.H.S = $\int \int \left(\nabla X\:F\right).n\ ds$ = $\frac{a^{3} }{2}$

Step-by-step explanation: