Use the transformation u = x − 2 y , υ = 2 x + y to find ∬ R x − 2 y 2 x + y d A where R is the rectangular region enclosed by the lines x − 2 y = 1 , x − 2 y = 4 , 2 x + y = 1 , 2 x + y = 3.
Use the transformation u = x − 2 y , υ = 2 x + y to find ∬ R x − 2 y 2 x + y d A where R is the rectangular region enclosed by the lines x − 2 y = 1 , x − 2 y = 4 , 2 x + y = 1 , 2 x + y = 3.
Use the transformation
u
=
x
−
2
y
,
υ
=
2
x
+
y
to find
∬
R
x
−
2
y
2
x
+
y
d
A
where R is the rectangular region enclosed by the lines
x
−
2
y
=
1
,
x
−
2
y
=
4
,
2
x
+
y
=
1
,
2
x
+
y
=
3.
Use the transformation u = y – 3x, v = y + 6x to evaluate
// (2y + 12x) dA on the parallelogram R with sides
R
y = 3x + 3, y = 3x + 12, y = –6x – 24, and y = -6x – 18.
(x – 2y) dA on the parallelogram P bounded by y = 5 – 2x, y = 7– 2x, y = 3x – 6, and y = 3x + 2. Use a change of variables
Evaluate
in order to integrate on an appropriate rectangle. Write the exact answer. Do not round.
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Use an appropriate change of variables to compute
SS. (x – y)e(x²-y²)dA
where R is the rectangle enclosed by the lines y = x, y = x-2, y = -x, and y = -x+2.
Chapter 14 Solutions
Calculus Early Transcendentals, Binder Ready Version
Precalculus: Mathematics for Calculus (Standalone Book)
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