Question

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)

Answer #1

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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 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 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.
(x −
8y) dA,
R
where R is the triangular region with vertices (0, 0),
(7, 1), and (1, 7).
x = 7u +
v, y = u +
7v

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.
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. 6y2 dA, R
where R is the region bounded by the curves xy = 3, xy = 6, xy2 = 3
and xy2 = 6; u = xy, v = xy2

2. Evaluate the double integral Z Z R e ^(x^ 2+y ^2) dA where R
is the semicircular region bounded by x ≥ 0 and x^2 + y^2 ≤ 4.
3. Find the volume of the region that is bounded above by the
sphere x^2 + y^2 + z^2 = 2 and below by the paraboloid z = x^2 +
y^2 .
4. Evaluate the integral Z Z R (12x^ 2 )(y^3) dA, where R is the
triangle with vertices...

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

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