Using Change of Variables..Evaluate ∫∫ R 15y/x dA where R is the region bounded by xy = 2, xy = 6 , y = 4 and y =10 using
the transformation x=v , y=2u/3v.
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Using Change of Variables.. Evaluate ∫∫ R 15y/x dA where R is the region bounded by xy = 2, xy = 6 , y = 4 and y =10 using the transformation x=v , y=2u/3v.
3. Use the transformation u = xy, v = y to evaluate the integral ∫∫R xy dA, where R is the ay region in the first quadrant bounded by the lines y = x and y = 3x, and the hyperbolas xy = 1, xy = 3
1/3 x + y 7. Consider dA where R is the region bounded by the triangle with vertices (0,0), (2,0), V= x+y X-y and (0,-2). The change of variables u=- defines a transformation T(x,y)=(u,v) from the xy-plane 2 to the uv-plane. (a) (10 pts) Write S (in terms of u and v) using set- builder notation, where T:R→S. Use T to help you sketch S in the uv-plane by evaluating T at the vertices. - 1 a(u,v) (b) (4 pts)...
9. (10 points) Evaluate S SR(2x2 - xy - y2)dA, where R is the region bounded by y = -2x +4, y = -2x + 7, y = x - 2, and y = 1 +1.
Use a change of variables to find the volume of the solid region lying below the surface -f(x, y) and above the plane region R x, y)xy)e- R: region bounded by the square with vertices (4, 0), (6, 2), (4, 4), (2, 2) Use a change of variables to find the volume of the solid region lying below the surface -f(x, y) and above the plane region R x, y)xy)e- R: region bounded by the square with vertices (4, 0),...
QUESTION 4 Use the appropriate transformation to evaluate SX (2x + y)(x - y)dA where R is the region bounded by the line y = 4 - 2x, y = 7 - 2x, y = x - 2 and y = x +1. (8 marks)
Use the given transformation to evaluate the integral. 10xy da, where is the region in the first quadrant bounded by the lines y = 1x and y = 3x and the hyperbolas xy - 3 and xy = 3; xu/v, y v
Calculate the integral using the type II method after the transformation: = SSR xy dA, where R is the region in the first quadrant bounded by the lines y = x, y = 3x, and the hyperbolas xy = 1, xy = 3. Make the transformation x = u/v and y = v
3. (A) (Change of Variables) Evaluate the following integrals by making appropriate change of variables. (a) // sin(x2 + y2) dA, where R is the region in the first quadrant bounded by the circle x2 + y2 = 5. YdA, where R is the parallelogram enclosed by the four lines 3. -Y x - 2y = 0, 2 - 2y = 4, 3.x - y = 1, and 3.c - y = 8. zevky / dA, where R is the...
Calculate the integral using the type II method after the transformation: 1 = SR xy da, where R is the region in the first quadrant bounded by the lines y = x, y = 3x, and the hyperbolas xy = 1, xy = 3. Make the transformation x = u/v and y = v
2. (35pt)Evaluate SS 3xy²dA, where R is the region bounded by the graphs of y = -x and y = x2, x > 0 and the graph of x = = 1. R