Evaluate the Surface Integral of G Over the Surface S $x + y + z = 1$

question 185

Multiple Choice

Evaluate the surface integral of G over the surface S.
-S is the plane $x + y + z = 1$ above the rectangle $0 \leq x \leq 3$ and $0 \leq y \leq 5 ; G ( x , y , z ) = 6 z$

• A) 360
• B) \(180 \sqrt { 3 }\)
• C) \(- 270 \sqrt { 3 }\)
• D) \(- 180\)

---

Definitions:

Color Perception

The process by which the brain interprets wavelengths of light as different colors, relying on the interactions of photoreceptor cells in the eyes.

Form Perception

The cognitive process of recognizing and identifying objects' shapes and structures in the environment.

Prosopagnosia

A neurological condition characterized by the inability to recognize faces, also known as face blindness.

Visual-form Agnosia

A neurological condition where a person can see objects but cannot recognize their shape, leading to an inability to identify the objects based on their forms.