Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Example// Find the volume enclosed by two surfaces Z1=2+x² +y2 ,Z2=4-x² - y² Solution // Z1 Z2 2+x² + y² = 4x² - y² 2 + x² + y² - 4 + x² + y² = 0 2x²+2y2 2 0 x² + y² = 1 ↔ x² + y² = p²² y=√1-x² Y2=-√√1-x= Volume=ff zdA=ff z dy dx = ff (Z2 - Z1) dy dx = (4 x2 y2-2-x² - y²) dy dx Volume-2 √1-2 (2- 2x² - 2y²)dy dx Or Volume-(2- 2x² – 2y²)dy dx Or Volume-41-2 ( (2-2x²-2y2)dy dx v=4 - 4 √² (2y – 2x² y — ²x²³)| √1-x² dx - = 4 + ſo (2√1 − x² - 2x² (1 − x²) - -2x²(1-x²) 2 (√1 = x²)³) dx 2(√1-x2)3 - 3

Example// Find the volume enclosed by two surfaces Z1=2+x² +y2 ,Z2=4-x² - y² Solution // Z1 Z2 2+x² + y² = 4x² - y² 2 + x² + y² - 4 + x² + y² = 0 2x²+2y2 2 0 x² + y² = 1 ↔ x² + y² = p²² y=√1-x² Y2=-√√1-x= Volume=ff zdA=ff z dy dx = ff (Z2 - Z1) dy dx = (4 x2 y2-2-x² - y²) dy dx Volume-2 √1-2 (2- 2x² - 2y²)dy dx Or Volume-(2- 2x² – 2y²)dy dx Or Volume-41-2 ( (2-2x²-2y2)dy dx v=4 - 4 √² (2y – 2x² y — ²x²³)| √1-x² dx - = 4 + ſo (2√1 − x² - 2x² (1 − x²) - -2x²(1-x²) 2 (√1 = x²)³) dx 2(√1-x2)3 - 3

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
Please (re)solve the questions below in some detail.......
Example// Find the volume enclosed by two surfaces Z1=2+x² +y2 ,Z2=4-x² - y² Solution // Z1 Z2 2+x² + y² = 4x² - y² 2 + x² + y² - 4 + x² + y² = 0 2x²+2y2 2 0 x² + y² = 1 ↔ x² + y² = p²² y=√1-x² Y2=-√√1-x= Volume=ff zdA=ff z dy dx = ff (Z2 - Z1) dy dx = (4 x2 y2-2-x² - y²) dy dx Volume-2 √1-2 (2- 2x² - 2y²)dy dx Or Volume-(2- 2x² – 2y²)dy dx Or Volume-41-2 ( (2-2x²-2y2)dy dx v=4 - 4 √² (2y – 2x² y — ²x²³)| √1-x² dx - = 4 + ſo (2√1 − x² - 2x² (1 − x²) - -2x²(1-x²) 2 (√1 = x²)³) dx 2(√1-x2)3 - 3
Transcribed Image Text:Example// Find the volume enclosed by two surfaces Z1=2+x² +y2 ,Z2=4-x² - y² Solution // Z1 Z2 2+x² + y² = 4x² - y² 2 + x² + y² - 4 + x² + y² = 0 2x²+2y2 2 0 x² + y² = 1 ↔ x² + y² = p²² y=√1-x² Y2=-√√1-x= Volume=ff zdA=ff z dy dx = ff (Z2 - Z1) dy dx = (4 x2 y2-2-x² - y²) dy dx Volume-2 √1-2 (2- 2x² - 2y²)dy dx Or Volume-(2- 2x² – 2y²)dy dx Or Volume-41-2 ( (2-2x²-2y2)dy dx v=4 - 4 √² (2y – 2x² y — ²x²³)| √1-x² dx - = 4 + ſo (2√1 − x² - 2x² (1 − x²) - -2x²(1-x²) 2 (√1 = x²)³) dx 2(√1-x2)3 - 3
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 4 images

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