Question

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

Answer #1

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

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 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.
(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.
(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)

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

Use the given transformation to evaluate the integral.
10x2dA,
R
where R is the region bounded by the ellipse
4x2 +
25y2 = 100;
x = 5u, y
= 2v

Use the given transformation to evaluate the integral.
8x2dA,
R
where R is the region bounded by the ellipse
25x2 +
36y2 = 900;
x = 6u, y =
5v

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