Chapter 16.8, Problem 10E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Use Stokes’ Theorem to evaluate ∫_{c}**F** · *d*r*.* In each Case *C* is oriented counterclockwise as viewed from above.

**10. F**(*x*, *y*, *z*) *=* 2*y* **i** + *xz* **j** + (*x* + *y*) **k**, *C* is the curve of intersection of the plane *z* = *y* + 2 and the cylinder *x*^{2} + *y*^{2} = l

To determine

**To evaluate**: The value of

Explanation

**Given data:**

The field is
*C* is curve of intersection of plane

**Formula used:**

Write the expression for curl of

Write the expression for the Stokesâ€™ theorem.

Here,

*S* is the surface.

Consider surface *S*,
*S*.

Here,

*A* is the area.

Find the value of

The surface *S* is a region which is enclosed by plane *C*. The expression for surface *S*,

Here,

Hence the equation is in the form of

The curve *C* is oriented in counter-clockwise, so orient the surface *S* in upwards.

Compare the equations

Find the value of

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