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11th Edition

Ron Larson + 1 other

Publisher: Cengage Learning

ISBN: 9781337275378

Chapter 15.6, Problem 31E

Textbook Problem

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Evaluating a Flux Integral In Exercises 31 and 32, find the flux of F over the closed surface. (Let N be the outward unit normal vector of the surface.)

To determine

**To calculate:** The flux of

**Given:**

The surface,

**Formula used:**

The gradient of

**Calculation:**

Let *S* be the portion of the plane,

Then,

The gradient of

Since the upward unit normal vector is defined as:

Then,

Therefore,

Multivariable Calculus

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Heat Flux Consider a single heat source located at...Ch. 15 - Heat Flux Consider a single heat source located at...Ch. 15 - Moments of Inertia Consider a wire of density...Ch. 15 - Moments of Inertia Using the formulas from...Ch. 15 - Laplace's Equation Let F(x,y,z)=xi+yj+zk, and let...Ch. 15 - Greens Theorem Consider the line integral...Ch. 15 - Area Use a line integral to find the area bounded...Ch. 15 - Area Use a line integral to find the area bounded...Ch. 15 - Work The force field F(x,y)=(x+y)i+(x2+1)j acts on...Ch. 15 - Work The force field F(x,y)=3x2y2i+2x3yj is shown...Ch. 15 - Area and Work How does the area of the ellipse...Ch. 15 - Verifying Identities (a) Let f and g be scalar...

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