Chapter 16.8, Problem 6E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Use Stokes’ Theorem to evaluate ∫∫* _{s}* curl F ·

**6. F**(*x*, *y*, *z*) = *e ^{xy}*

To determine

**To evaluate**: The expression

Explanation

**Given data:**

Consider the expression for the vector field

And *S* is the half of the ellipsoid that is,

**Formula Used:**

Consider the expression for the Stokesâ€™ theorem,

Consider the boundary curve *C* is the circle
*C* must be oriented in the counter-clockwise direction when viewed from the right. Therefore, the vector equation of *C* is,

Differentiate the equation with respect to *t*.

Find the expression for

Substitute
*x*,
*y* and
*z* in equation (1) to find

Write the expression for the Stokesâ€™ theorem in equation (3),

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