UM The Volume of A Region Delimited by Area Analysis

Post ID: 2240303

Overview

I'm working on a calculus exercise and need an explanation and answer to help me learn.

We consider a region E of space delimited by a closed, piecewise smooth surface S.

???? V 1 3 (cz+ y+ zhi.ds. y 2 3 S

a) Use the formula of V to calculate the volume of the region delimited by the area parameterized by : ?(u, v) = (1+u) cos(u) 7 + (1 – u) sin(v) 7 +(1+u) k, -1 SuS1, -A SUST << -a < = -

and shown below :

2 1.5 2 1- 0.5- -2 - 1 -2 0 -1 0 - ? 2 ?

b) The following question is independent of part a). Show that the flux through a closed surface of a vector field of the form

F(x, y, z) = [ax + A?y,z)] 7 + [by + B(x, z)]] + [cz +C(x, y)] k, = 2

where a, b, c are constants and A, B, C are functions, is proportional to the volume of the region inside the surface.