Evaluate. The differential is exact.
-$$\int _ { ( 1,1,1 ) } ^ { ( 5,3,4 ) } \frac { 1 } { x } d x + \frac { 1 } { y } d y + \frac { 1 } { z } d z$$
A) ln 60
B) ln 20
C) ln 12
D) 0

Question

Quizplus · Accepted Answer

The integral of an exact differential $\frac{1}{x}dx + \frac{1}{y}dy + \frac{1}{z}dz$ from $(1,1,1)$ to $(5,3,4)$ is $\ln\left(\frac{5}{1}\right) + \ln\left(\frac{3}{1}\right) + \ln\left(\frac{4}{1}\right) = \ln(5 \times 3 \times 4) = \ln(60)$.

Evaluate the Differential Is Exact ∫(1,1,1)(5,3,4)1xdx+1ydy+1zdz\int _ { ( 1,1,1 ) } ^ { ( 5,3,4 ) } \frac { 1 } { x } d x + \frac { 1 } { y } d y + \frac { 1 } { z } d z∫(1,1,1)(5,3,4)​x1​dx+y1​dy+z1​dz

Evaluate the Differential Is Exact $\int _ { ( 1,1,1 ) } ^ { ( 5,3,4 ) } \frac { 1 } { x } d x + \frac { 1 } { y } d y + \frac { 1 } { z } d z$