Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
In Exercises 10-12 use (4) or (6) to evaluate ſſ F · n dS. 10. F(x, y, z) = yi − xj + 8k; Σ is the part of the paraboloid z=9-x²² above the xy plane; n is directed upward. 11. F(x, y, z) = xi − j + 2x²k; Σ is the part of the paraboloid z = x² + 12² above the region in the xy plane bounded by the parabolas x = 1 − y² and x = y² – 1; n is directed downward. - 12. F(x, y, z) = xi + yj + zk; Σ is the cube with vertices (0, 0, 0), (0, 0, 1), (0, 1, 0), (0, 1, 1), (1, 0, 0), (1, 0, 1), (1, 1, 0), and (1, 1, 1); n is directed outward from the cube.

In Exercises 10-12 use (4) or (6) to evaluate ſſ F · n dS. 10. F(x, y, z) = yi − xj + 8k; Σ is the part of the paraboloid z=9-x²² above the xy plane; n is directed upward. 11. F(x, y, z) = xi − j + 2x²k; Σ is the part of the paraboloid z = x² + 12² above the region in the xy plane bounded by the parabolas x = 1 − y² and x = y² – 1; n is directed downward. - 12. F(x, y, z) = xi + yj + zk; Σ is the cube with vertices (0, 0, 0), (0, 0, 1), (0, 1, 0), (0, 1, 1), (1, 0, 0), (1, 0, 1), (1, 1, 0), and (1, 1, 1); n is directed outward from the cube.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question

Practice problem taken from Denny Gulick, Robert Ellis - Calculus With Concepts in Calculus. Sixth-Cengage Learning, chapter 15.6. Requesting help with number 12.
Please show and explain ALL steps; I'm trying to practice for an exam and need help understanding this. Do not use Stokes Theorem, or Divergence Theorem, as that's not covered until the following 2 chapters.

In Exercises 10-12 use (4) or (6) to evaluate ſſ F · n dS. 10. F(x, y, z) = yi − xj + 8k; Σ is the part of the paraboloid z=9-x²² above the xy plane; n is directed upward. 11. F(x, y, z) = xi − j + 2x²k; Σ is the part of the paraboloid z = x² + 12² above the region in the xy plane bounded by the parabolas x = 1 − y² and x = y² – 1; n is directed downward. - 12. F(x, y, z) = xi + yj + zk; Σ is the cube with vertices (0, 0, 0), (0, 0, 1), (0, 1, 0), (0, 1, 1), (1, 0, 0), (1, 0, 1), (1, 1, 0), and (1, 1, 1); n is directed outward from the cube.
Transcribed Image Text:In Exercises 10-12 use (4) or (6) to evaluate ſſ F · n dS. 10. F(x, y, z) = yi − xj + 8k; Σ is the part of the paraboloid z=9-x²² above the xy plane; n is directed upward. 11. F(x, y, z) = xi − j + 2x²k; Σ is the part of the paraboloid z = x² + 12² above the region in the xy plane bounded by the parabolas x = 1 − y² and x = y² – 1; n is directed downward. - 12. F(x, y, z) = xi + yj + zk; Σ is the cube with vertices (0, 0, 0), (0, 0, 1), (0, 1, 0), (0, 1, 1), (1, 0, 0), (1, 0, 1), (1, 1, 0), and (1, 1, 1); n is directed outward from the cube.
Expert Solution
steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS