Vector Calculus

Given that $\vec{F}(x, y, z) = \sin(y) \hat{x} + \cos(x) \hat{y} + 5 \hat{z}$, the integral $\oiint_S \vec{F}(x, y, z) \cdot d\vec{s}$ over the unit sphere S centered at the origin evaluates to ________ (Round off to one...

The closed curve shown in the figure is described by r = 1 + cosθ, where r = √x² + y²; x = rcosθ, y = rsinθ The magnitude of the line integral of the vector field F = -yî + xĵ around the closed curve is ________ (Round o...