"The value of `(x^2(yz)^2)/((xz)^2y^2)(y^2(xz)^2)/((xy)^2z^2)(z^2(xy)^2)/((yz)^2x^2)`is`1`(b) 0 (c) 1 (d) None of these"This integral of a function along a curve C is often written in abbreviated form as ∫ C f ( x, y) d s Example 1621 Compute ∫ C y e x d s where C is the line segment from ( 1, 2) to ( 4, 7) We write the line segment as a vector function r = 1, 2 t 3, 5 , 0 ≤ tThe sphere x2 y 2 z = 16 and outside the cylinder x2 y = 4 Solution The sphere x2 y2 z2 = 16 intersects the xyplane along the circle with equation x 2 y = 16 Since the solid is symmetric about the xyplane, we may compute its total volume as twice the volume of the part that lies above the xyplane, and this
The Divergence Theorem
