(Chapter 17,Section 19.1) Consider the region R bounded by the lines y = −3x and Y = 3x and the parabola y = 4 – x². (a) Find a 2-dimensional vector field F = (M(x, y), N(x, y)) such that ƏM ƏN əx ду = 1. (b) Using this F and Green's theorem (Theorem 19.1.1), write the area integral a line integral. [Hint: Any function y = ƒ(x) can be parametrised by r(t) = (t, f(t)). This can be used to parametrise both the line and the parabola]. (c) Using this line integral find the area of B 1 dA as
(Chapter 17,Section 19.1) Consider the region R bounded by the lines y = −3x and Y = 3x and the parabola y = 4 – x². (a) Find a 2-dimensional vector field F = (M(x, y), N(x, y)) such that ƏM ƏN əx ду = 1. (b) Using this F and Green's theorem (Theorem 19.1.1), write the area integral a line integral. [Hint: Any function y = ƒ(x) can be parametrised by r(t) = (t, f(t)). This can be used to parametrise both the line and the parabola]. (c) Using this line integral find the area of B 1 dA as
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![(Chapter 17, Section 19.1)
Consider the region R bounded by the lines y = −3x and y = = 3x and the parabola y = 4 − x².
(a) Find a 2-dimensional vector field F = (M (x, y), N(x, y)) such that
ƏN
ӘМ
əx
ду
1.
JJ₁²
(b) Using this F and Green's theorem (Theorem 19.1.1), write the area integral
a line integral.
[Hint: Any function y = f(x) can be parametrised by r(t) = (t, f(t)). This can be used to
parametrise both the line and the parabola].
(c) Using this line integral, find the area of R.
1 dA as](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8d4b7300-85f6-4fda-bf3b-5d34dbcdb2ca%2F869d1fda-d309-4958-90cf-0b3abfdb9d5f%2F2ou2rs_processed.png&w=3840&q=75)
Transcribed Image Text:(Chapter 17, Section 19.1)
Consider the region R bounded by the lines y = −3x and y = = 3x and the parabola y = 4 − x².
(a) Find a 2-dimensional vector field F = (M (x, y), N(x, y)) such that
ƏN
ӘМ
əx
ду
1.
JJ₁²
(b) Using this F and Green's theorem (Theorem 19.1.1), write the area integral
a line integral.
[Hint: Any function y = f(x) can be parametrised by r(t) = (t, f(t)). This can be used to
parametrise both the line and the parabola].
(c) Using this line integral, find the area of R.
1 dA as
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