By the change of variable x(u, v) = uv, y(u, v) = u/v is double integral, the integrand f(x, y) change to.Then,φ(u,v) isa)2u/vb)1c)2uvd)v2Correct answer is option 'A'. Can you explain this answer?

Question

By the change of variable x(u, v) = uv, y(u, v) = u/v is double integral, the integrand f(x, y) change to.Then,&phi;(u,v) isa)2u/vb)1c)2uvd)v2Correct answer is option 'A'. Can you explain this answer?

Answer

Step 1: Calculate Partial Derivatives

Given:

We find the partial derivatives as follows:

Step 2: Set Up the Jacobian Determinant

Step 3: Calculate the Determinant

The absolute value of J (since we are only concerned with the magnitude in the context of integration) is:

Conclusion: The value of ϕ(u, v) is: a. 2u/v

Similar Mathematics Doubts

By a change of variable x(u,v) = uv, y(u,v) = v/u is double integral, the integrand f(x,y) change to f(uv, v/u)φ(u,v). Thenφ (u,v) is

Value of the integralwhere C is thesquare cut from the first quadrant by the lines x = 1 and y = 1 will be (use Green’s theorem to change the line integral into double integral)

Value of the integralwhere C is the square cut from the first quadrant by the lines x = 1 and y = 1 will be (use Green’s theorem to change the line integral into double integral)

Let F(x) be the particular integral of the differential equation, y” +y = sec 2x Then F(0) is equal to________ . Correct answer is '1'. Can you explain this answer?

Consider the function f, defined by f(x)= x x ^ 2 for rational x and , x^ 2 x^ 3 for irrational x .Let I= Lower Reimann integral, J = Upper Riemann integral. Then what will be value of I and J? (

Top Courses for Mathematics

Suggested Free Tests

Related Content

Schools

Competitive Examinations

Quick Access Links

Technical Exams