Evaluate $\iint _ { S } f ( x , y , z ) d S$.
$f ( x , y , z ) = 2 x + 2 y + 5 z ; S$ is the part of the cone $z = \sqrt { x ^ { 2 } + y ^ { 2 } }$ between the planes $z = 1$ and $z = 2$.
A) $70 \pi \sqrt { 2 }$
B) $70 \sqrt { 2 }$
C) $\frac { 70 } { 3 } \pi \sqrt { 2 }$
D) 0

Question

Quizplus · Accepted Answer

The integral is evaluated over the surface of a cone between two planes. The surface integral can be computed using cylindrical coordinates, and the result is $\frac { 70 } { 3 } \pi \sqrt { 2 }$.

Evaluate ∬Sf(x,y,z)dS\iint _ { S } f ( x , y , z ) d S∬S​f(x,y,z)dS

Evaluate $\iint _ { S } f ( x , y , z ) d S$