Question

Given the set S = {(u,v): 0<= u<=4 and 0<= v<=3} and the transformation T(u, v) = (x(u, v), y(u, v)) where x(u, v) = 4u + 5v and y(u, v) = 2u -3v,

graph the image R of S under the transformation T in the xy-plan

and find the area of region R

Answer #1

Let the linear transformation T: V--->W be such that T (u) =
u2 If a, b are Real. Find T (au + bv) ,
if u = (x, y) v = (z, w) and uv = (xz-yw, xw + yz)
Let the linear transformation T: V---> W be such that T (u)
= T (x, y) = (xy, 0) where u = (x, y), with 2, -3. Then, if u = (
1.0) and v = (0.1). Find the value...

Use the given transformation to evaluate the integral.
(x −
6y) dA,
R
where R is the triangular region with vertices (0, 0),
(5, 1), and (1, 5).
x = 5u +
v, y = u +
5v

Use the given transformation to evaluate the double integral of
(x-6y) dA, where R is the triangular region with vertices
(0, 0), (5, 1), and (1, 5).
x = 5u +
v, y = u +
5v

Use the given transformation to evaluate the integral.
3x2dA,
R
where R is the region bounded by the ellipse
25x2 +
4y2 = 100;
x = 2u,
y = 5v

Find∫∫R(2x+4y)dA where RR is the parallelogram with vertices
(0,0), (-4,2), (5,4), and (1,6).
Use the transformation x=−4u+5v , y=2u+4v

Use the given transformation to evaluate the integral. (15x +
15y) dA R , where R is the parallelogram with vertices (−1, 4), (1,
−4), (2, −3), and (0, 5) ; x = 1 5 (u + v), y = 1 5 (v − 4u)

Use the given transformation to evaluate the integral.
6xy dA
R
, where R is the region in the first quadrant bounded
by the lines y =
2
3
x and y =
3
2
x and the hyperbolas xy =
2
3
and xy =
3
2
;
x = u/v, y = v

Use the given transformation to evaluate the integral.
6xy dA
R
, where R is the region in the first quadrant bounded
by the lines y =
1
2
x and y =
3
2
x and the hyperbolas xy =
1
2
and xy =
3
2
;
x = u/v, y = v

Use the given transformation to evaluate the integral.
(12x + 12y) dA
R
, where R is the parallelogram with vertices
(−2, 4),
(2, −4),
(5, −1),
and
(1, 7)
; x =
1
3
(u + v), y =
1
3
(v − 2u)

Use the given transformation to evaluate the double integral.
(12x + 12y) dA R , where R is the parallelogram with vertices (−3,
6), (3, −6), (4, −5), and (−2, 7) ; x = 1/ 3 *(u + v), y = 1 /3* (v
− 2u)

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