Explanation Let the vector field be F → = 2 x i ^ − 3 y j ^ and S is the part of the hemisphere z = 1 − x 2 − y 2 x 2 + y 2 + z 2 = 5 for z ≥ 1 . We will use the divergence theorem, so div F ^ = ∂ ∂ x ( 2 x ) + ∂ ∂ y ( − 3 y ) + ∂ ∂ z ( 0 ) = 2 − 3 = − 1 Thus, ∬ S F → ⋅ N → d S = ∭ R div F ^ d V = ∫ − 5 5 ∫ − 5 − x 2 5 − x 2 ∫ 1 5 − x 2 − y 2 ( − 1 ) d z d y d x = − ∫ − 5 5 ∫ − 5 − x 2 5 − x 2 [ z ] 1 5 − x 2 − y 2

6th Edition

ISBN: 9781465208880

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

See similar textbooks

Videos

Question

Chapter 13.5, Problem 38PS

To determine

To calculate: The value of the integral ∬SF→⋅N→dS for the vector field F→=2xi^−3yj^ and S is the part of the hemisphere x2+y2+z2=5 for z≥1 .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13.5, Problem 37PS

Chapter 13.5, Problem 39PS

Students have asked these similar questions

Incorrect. Use a computer or calculator with Euler's method to approximate the flow line through (1, 2) for the vector field v = y² i + 1.1x² j using 5 steps with At = 0.1. Find the exact values of x1,.…. ,X5 and yı, , y5 and then fill in the blanks rounding your numbers to •.... three decimal places. X1 = i 1.1 ,Yi = i 2.51 X2 i 1.2 ,y2 3.273 X3 = i 1.3 ,Y3 = i 4.50283 X4 = i 1.4 , Y4 i 6.7162 X5 = i 1.5 , Y5 = i 11.4427 eTextbook and Media Hint I| ||

Incorrect. Use a computer or calculator with Euler's method to approximate the flow line through (1, 2) for the vector field v = y² i +1.1x² j using 5 steps with At = 0.1. Find the exact values of x1, ... , x5 and y1, ... , y5 and then fill in the blanks rounding your numbers to three decimal places. X1 = !Yı = i X2 i 1.2 , y2 3.273 X3 = i 1.3 Y3 = i 4.50283 X4 i 1.4 6.7162 X5 = i 1.5 Y5 = i 11.4427 eTextbook and Media Assistance Used Hint Assistance Used The vector field is given by v = y i + 1.1x² j , that is, the flow line (x (t), y (t)) satisfies x' (t) = y² y' (t) = 1.1x².

A4. Which of the following vector fields is not the curl of another vector field? A. F=zi+zj+yk B. F= ²1-2ryj+5k C. F=3ri-2yj-zk D. F=zi+yj+zk E. F= 21+2+4k Conti

Chapter 13 Solutions

Calculus

Ch. 13.1 - Prob. 1PS Ch. 13.1 - Prob. 2PS Ch. 13.1 - Prob. 3PS Ch. 13.1 - Prob. 4PS Ch. 13.1 - Prob. 5PS Ch. 13.1 - Prob. 6PS Ch. 13.1 - Prob. 7PS Ch. 13.1 - Prob. 8PS Ch. 13.1 - Prob. 9PS Ch. 13.1 - Prob. 10PS

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The value of the integral ∬ S F → ⋅ N → d S for the vector field F → = 2 x i ^ − 3 y j ^ and S is the part of the hemisphere x 2 + y 2 + z 2 = 5 for z ≥ 1 .

Solution Summary: The author calculates the value of the integral displaystyle 'underset'Siint'sstackreltoFcdot

Videos

To calculate: The value of the integral ∬SF→⋅N→dS for the vector field F→=2xi^−3yj^ and S is the part of the hemisphere x2+y2+z2=5 for z≥1 .

Want to see the full answer?

Chapter 13 Solutions