Calc Jacobian

posted by .

Thanks

"I know that the xy region is the line x=y y=0 and y=1- x/2)"



It is helpful to rewrite the region in the x-y plane by specifying the three lines and the endpoints, i.e. the points where they intersect.

If you insert these points in the formula for U and V you obtain the vertices in the U-V plane.

E.g., the line x = y maps to the line
V = 0. But in the x-y plane this line is bounded by the "end points" (x=0,y=0) and (x=2/3,y=2/3) which in the U-V plane has coordinates (U = 0, V = 0) and (U = 2, V = 0) respectively.

I need to find out how to solve this integral with the indicated changes.

int.[0 to 2/3]int[y to 2-2y]
(x+2y)e^(y-x)
dxdy

u=x+2y v=x-y

I know that the xy region is the line x=y y=0 and y=1- x/2)

but when I make the changes, I don't get a new region bounded by graphs.

Can anyone see a way to solve this one?

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    I am a little lost on my homework can someone help me with these problems please! With a GM MasterCard, 5% of the amount charged is credited toward a rebate on the purchase of a new car. Express the R as a function of the amount charged …
  2. Algebra

    Write a system of inequalities to express the exterior of the triangle ABD if A=(-2,7), B=(4,0), and C=(1,-3). Please help! gracias<3 Derive equations for the three lines connecting the three points. Then change the equations to …
  3. MATH

    Region A that on xy-plane is bounded by two (2) curves and a line. The curves are y=x^3-2x+3 and y=-x^2+3 while the line is x=0. It is located in the first quadrant of xy-plane. Determine the area of region A.
  4. Calculus

    1. Find the area of the region bounded by the curves and lines y=e^x sin e^x, x=0, y=0, and the curve's first positive intersection with the x-axis. 2. The area under the curve of y=1/x from x=a to x=5 is approximately 0.916 where …
  5. Calc II

    Find the volume of the solid generated by rotating the region of the x-y plane between the line y=6, the curve y=3sin(x)+3 for -pi/2 < (or equal to) x < (or equal to) 5pi/2 about the line y = 6.
  6. Calculus (Jacobian question)

    Evaluate double integral ln((x-y)/(x+y)) dy dx where the double integral region is the triangle with vertices (1,0),(4,3), (4,1). Hint: use a transformation with the Jacobian.
  7. Biology

    Four different molecules are shown below. For each, indicate if it would be found in region A, B, C, and D. An image of the structure of glucose. Molecule Found in Region A Found in Region B Found in Region C Found in Region D An image …
  8. history

    1. The region of the United States in which Georgia is located is the (1 point) northeastern region. southeastern region. northwestern region. southwestern region.
  9. S.S

    1)The region of the United States in which Georgia is located is the?
  10. Calc 2

    Use the shell method to find the volume of the solid generated by revolving the region bounded by the line y = x + 2 and the parabola y = x^2 about the following lines: a) The line x=2 b) The line x=-1 c) The x axis d) The line y=26 …

More Similar Questions