Evaluate $\iint _ { S } f ( x , y , z ) d S$ . $f ( x , y , z ) = x + y$ ; S is the part of the plane $7 x + 3 y + z = 21$ in the first octant.
A) 0
B) $\sqrt { 327 }$
C) $35$ $\sqrt { 59 }$
D) $2 \sqrt { 139 }$

Question

Quizplus · Accepted Answer

The integral evaluates the surface integral of the function $f(x, y, z) = x + y$ over the plane $7x + 3y + z = 21$ in the first octant. The limits for $x$ and $y$ are determined by the intercepts of the plane with the axes. The correct evaluation of the integral gives $35 \sqrt{59}$.

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

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