?Show that F is conservative and use this fact to evaluate ?C F dr along the given

Chapter 16, Problem 14

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QUESTION:

Show that F is conservative and use this fact to evaluate ∫C F  dr along the given curve.

F(x, y, z) = ey i + (xey + ez) j + yez k,

C is the line segment from (0, 2, 0) to (4, 0, 3)

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QUESTION:

Show that F is conservative and use this fact to evaluate ∫C F  dr along the given curve.

F(x, y, z) = ey i + (xey + ez) j + yez k,

C is the line segment from (0, 2, 0) to (4, 0, 3)

ANSWER:

Step 1 of 6

According to the definition of curl,

Where,

For to be conservative,

Which get simplified to following expression:

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