Use the transformation u = x , υ = z − y , w = x y to find ∭ G z − y 2 x y d V where G is the region enclosed by the surfaces x = 1 , x = 3 , z = y + 1 , x y = 2 , x y = 4.
Use the transformation u = x , υ = z − y , w = x y to find ∭ G z − y 2 x y d V where G is the region enclosed by the surfaces x = 1 , x = 3 , z = y + 1 , x y = 2 , x y = 4.
Use the transformation
u
=
x
,
υ
=
z
−
y
,
w
=
x
y
to find
∭
G
z
−
y
2
x
y
d
V
where G is the region enclosed by the surfaces
x
=
1
,
x
=
3
,
z
=
y
+
1
,
x
y
=
2
,
x
y
=
4.
Use
the map G(u, v) = (v1)
a = 4, b = 8, c = 6.
b
a
y=cx
UD
v+1
Ø₂ (x +
(x + y) dx dy =
to compute (x + y) dx dy, where D is the shaded region in the figure. Assum-
y=x
X
(Use decimal notation. Give your answer to three decimal places.)
Use the cross product to find the area of the portion of the plane defined
by z = x + y which lies above the square [0, 1] x [0, 1] in the xy-plane. Draw
a picture.
Use the transformation u = x2 –- y²,v = x² + y² to find ff, xydA where R
is the region in the first quadrant that is enclosed by the hyperbolas x2
y² = 1, x² – y² = 4 and the circles x² + y? = 4 and x? + y? = 9.
Chapter 14 Solutions
Calculus Early Transcendentals, Binder Ready Version
Precalculus: Mathematics for Calculus - 6th Edition
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