Evaluate. The differential is exact.
-$$\int _ { ( 0,0,0 ) } ^ { ( 3,7,9 ) } ( 3 x + 1 ) e ^ { 3 x } d x + z d y + y d z$$
A) $3 \mathrm { e } ^ { 9 } + 64$
B) $3 e ^ { 9 } + 63$
C) $3 \mathrm { e } ^ { 9 } + 16$
D) 0

Question

Quizplus · Accepted Answer

The integral of an exact differential is the difference of the potential function evaluated at the endpoints. The potential function is $F(x, y, z) = e^{3x} + yz$. Evaluating at (3,7,9) and (0,0,0) gives $3e^9 + 63$.

Evaluate the Differential Is Exact ∫(0,0,0)(3,7,9)(3x+1)e3xdx+zdy+ydz\int _ { ( 0,0,0 ) } ^ { ( 3,7,9 ) } ( 3 x + 1 ) e ^ { 3 x } d x + z d y + y d z∫(0,0,0)(3,7,9)​(3x+1)e3xdx+zdy+ydz

Evaluate the Differential Is Exact $\int _ { ( 0,0,0 ) } ^ { ( 3,7,9 ) } ( 3 x + 1 ) e ^ { 3 x } d x + z d y + y d z$