Evaluate the integral.
-$$\int _ { 1 } ^ { \mathrm { e } ^ { 3 } } \int _ { 1 } ^ { \mathrm { e } ^ { 10 } } \int _ { 1 } ^ { \mathrm { e } ^ { 8 } } \frac { 1 } { \mathrm { xyz } } \mathrm { dx } d y \mathrm { dz }$$
A) 480
B) 720
C) 240
D) 80

Question

Quizplus · Accepted Answer

The integral can be evaluated by integrating step by step. First, integrate with respect to $x$, then $y$, and finally $z$. The integral of $\frac{1}{xyz}$ with respect to $x$ from 1 to $e^8$ is $\ln(e^8) = 8$, because $\int \frac{1}{x} dx = \ln|x|$. Then, integrate $8/y$ with respect to $y$ from 1 to $e^{10}$, which gives $8\ln(e^{10}) = 80$. Finally, integrate $80/z$ with respect to $z$ from 1 to $e^3$, which gives $80\ln(e^3) = 240$.

Evaluate the Integral A) 480 B) 720 C) 240 D) 80

Evaluate the Integral A) 480
B) 720
C) 240
D) 80