Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
1. Let F(x, y) = (1 — y, ½x³ +e³²), and let C with the position vector r be the portion of the parabola y = x² – 1 from (−1,0) to (1,0). Complete the following steps to determine the value of SF · dr. (a) Make a rough sketch of the curve C. Note that C is not closed, so we cannot apply Green's Theorem to calculate F. dr. Identify another curve C₂ that will make the combined curve Ỡ = CỤC₂ (i.e. C together with C₂) closed and positively oriented. Be sure to specify the orientation of C₂. (b) Use Green's Theorem to calculate ſ♂ F · dr. (c) Calculate fc, F. dr directly. (d) Now use the fact that ſ♂ F · . dr = ScF·dr + Sc₂ F·dr and your answers to the previous parts to calculate fF.dr.

1. Let F(x, y) = (1 — y, ½x³ +e³²), and let C with the position vector r be the portion of the parabola y = x² – 1 from (−1,0) to (1,0). Complete the following steps to determine the value of SF · dr. (a) Make a rough sketch of the curve C. Note that C is not closed, so we cannot apply Green's Theorem to calculate F. dr. Identify another curve C₂ that will make the combined curve Ỡ = CỤC₂ (i.e. C together with C₂) closed and positively oriented. Be sure to specify the orientation of C₂. (b) Use Green's Theorem to calculate ſ♂ F · dr. (c) Calculate fc, F. dr directly. (d) Now use the fact that ſ♂ F · . dr = ScF·dr + Sc₂ F·dr and your answers to the previous parts to calculate fF.dr.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 18T
See similar textbooks
icon
Related questions
Question
1. Let F(x, y) = (1 − y, x³ +e³²), and let C with the position vector r be the portion of the parabola y = x² – 1 from (−1,0) to (1,0). Complete the following steps to determine the value of F · dr. (a) Make a rough sketch of the curve C. Note that C is not closed, so we cannot apply Green's Theorem to calculate F. dr. Identify another curve C₂ that will make the combined curve Ĉ = CỤC₂ (i.e. C together with C₂) closed and positively oriented. Be sure to specify the orientation of C₂. (b) Use Green's Theorem to calculate fF.dr. (c) Calculate ₂ F. dr directly. (d) Now use the fact that fF.dr = F·dr + Sc₂ F. dr and your answers to the previous parts to calculate fF.dr.
Transcribed Image Text:1. Let F(x, y) = (1 − y, x³ +e³²), and let C with the position vector r be the portion of the parabola y = x² – 1 from (−1,0) to (1,0). Complete the following steps to determine the value of F · dr. (a) Make a rough sketch of the curve C. Note that C is not closed, so we cannot apply Green's Theorem to calculate F. dr. Identify another curve C₂ that will make the combined curve Ĉ = CỤC₂ (i.e. C together with C₂) closed and positively oriented. Be sure to specify the orientation of C₂. (b) Use Green's Theorem to calculate fF.dr. (c) Calculate ₂ F. dr directly. (d) Now use the fact that fF.dr = F·dr + Sc₂ F. dr and your answers to the previous parts to calculate fF.dr.
Expert Solution
steps

Step by step

Solved in 5 steps with 5 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
SEE MORE TEXTBOOKS