What is the Jacobian?

Question

a	Compute the Jacobian.
b	Change variables and evaluate the new integral.

Answer 1

J = I 5 0I = 10

I-1 2I∫

∫∫_Rx²√x + 5ydA = ∫∫_D25u²√10v·10dudv = D = {0 ≤ u ≤1, - u ≤ 2v - u ≤ 4 - 5u or 0 ≤ v ≤ 2 - 2u}

= ∫₀¹250√10u²du∫₀^2-2uv^1/2dv = 250√10∫₀¹2/3u²(2 - 2u)^3/2u²du = 500√100/3∫₀¹u²(2 - 2u)^3/2du = 75.7187

To evaluate last integral we used TI-84