Use stokes' theorem to evaluate c f · dr where c is oriented counterclockwise as viewed from above. f(x, y, z) = yzi + 4xzj + exyk, c is the circle x2 + y2 = 9, z = 3.use stokes' theorem to evaluate c f · dr where c is oriented counterclockwise as viewed from above. f(x, y, z) = yzi + 4xzj + exyk, c is the circle x2 + y2 = 9, z = 3.

The result of the integral is 81π

Step-by-step explanation:

We can use Stoke's Theorem to evaluate the given integral, thus we can write first the theorem:

Finding the curl of F.

Given we have:

Working with the determinant we get

Working with the partial derivatives

Integrating using Stokes' Theorem

Now that we have the curl we can proceed integrating

where the normal to the circle is just since the normal is perpendicular to it, so we get

Only the z-component will not be 0 after that dot product we get

Since the circle is at z = 3 we can just write

Thus the integral represents the area of a circle, the given circle has a radius r = 3, so its area is , so we get

Thus the result of the integral is 81π

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step-by-step explanation: there is no picture

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step-by-step explanation:

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