a) Find the Jacobian determinant(u, v)of u(r, y) = r+ y, v(x, y) = x – 2y.(x, y)b) Using (a) evaluate the integral(x+ y)*dxdywhere R is the plane region bounded by the linesx +y = 1, r+ y = 4, x – 2y = -2, x - 2y = 1.

a The Jacobin determinant of u and v is. ∂u,v∂x,y=∂u∂x∂u∂y∂v∂x∂v∂x Where ux,y=x+y , vx,y=x-2y…

O(u, 0) of u(r, y) = r + y, v(r, y) = x - 2y- a(r, y) a) Find the Jacobian determinant b) Using (a) evaluate the integral (x + y)*drdy where R is the plane region bounded by the lines x +y = 1, r+y = 4, r - 2y = -2, x – 2y = 1.

O(u, 0) of u(r, y) = r + y, v(r, y) = x - 2y- a(r, y) a) Find the Jacobian determinant b) Using (a) evaluate the integral (x + y)*drdy where R is the plane region bounded by the lines x +y = 1, r+y = 4, r - 2y = -2, x – 2y = 1.

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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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.

Question

a) Find the Jacobian determinant
(u, v)
of u(r, y) = r+ y, v(x, y) = x – 2y.
(x, y)
b) Using (a) evaluate the integral
(x+ y)*dxdy
where R is the plane region bounded by the lines
x +y = 1, r+ y = 4, x – 2y = -2, x - 2y = 1.

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