Question

For the force field given by extbf{F}(x, y, z) = e^x cos y extbf{i} - e^x sin y extbf{j} + 2 extbf{k} show that $int_C extbf{F} cdot d extbf{r}$ is independent of path, and calculate the work done by extbf{F} on an object moving along a curve C from $(0, frac{pi}{2}, 1)$ to $(1, pi, 3)$.

          For the force field given by
	extbf{F}(x, y, z) = e^x cos y 	extbf{i} - e^x sin y 	extbf{j} + 2	extbf{k}
show that $int_C 	extbf{F} cdot d	extbf{r}$ is independent of path, and calculate the work done by 	extbf{F} on an
object moving along a curve C from $(0, frac{pi}{2}, 1)$ to $(1, pi, 3)$.

$For the force field given by extbfF(x, y, z) = e^x cos y extbfi - e^x sin y extbfj + 2 extbfk show that intC extbfF cdot d extbfr is independent of path, and calculate the work done by extbfF on an object moving along a curve C from (0, fracpi2, 1) to (1, pi, 3).$

Added by Jodi D.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Supreeta N

08/02/2023

Step 1

First, we need to show that the given force field F is conservative, which means it is the gradient of a scalar potential function. To do this, we will check if the curl of F is zero. The curl of F is given by: $$\nabla \times \mathbf{F} = \begin{vmatrix} Show more…

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For the force field given by F(x, y, z) = e^x cos yi - e^x sin yj + 2k show that integral_C F . dr is independent of path, and calculate the work done by F on an object moving along a curve C from (0, pi/2, 1) to (1, pi, 3).