Find the volume under the surface z = f(x,y) and above the rectangle with the given boundaries.
-$$\mathrm { z } = \frac { \mathrm { x } } { \mathrm { y } } ; 0 \leq \mathrm { x } \leq 1,1 \leq \mathrm { y } \leq \mathrm { e }$$
A) $\frac { 1 } { 2 }$
B) $\frac { 1 } { 3 }$
C) $\frac { 1 } { 6 }$
D) $\frac { 1 } { 4 }$

Question

Quizplus · Accepted Answer

To find the volume under the surface $z = \frac{x}{y}$ and above the rectangle defined by $0 \leq x \leq 1$ and $1 \leq y \leq e$, we integrate the function over the given rectangle. The double integral is $\int_{1}^{e} \int_{0}^{1} \frac{x}{y} dx dy$. Solving this gives $\frac{1}{2}$.

Find the Volume Under the Surface Z = F(x,y) and Above