If a , b , and c are positive constants, then the transformation x = a u , y = b υ , z = c w can be rewritten as x / a = u , y / b = υ , z / c = w , and hence it maps the spherical region u 2 + υ 2 + w 2 ≤ 1 into the ellipsoidal region x 2 a 2 + y 2 b 2 + z 2 c 2 ≤ 1 In these exercises, perform the integration by transforming the ellipsoidal region of integration into a spherical region of integration and then evaluating the transformed integral in spherical coordinates. ∭ G x 2 d V , where G is the region enclosed by the ellipsoid 9 x 2 + 4 y 2 + z 2 = 36.
If a , b , and c are positive constants, then the transformation x = a u , y = b υ , z = c w can be rewritten as x / a = u , y / b = υ , z / c = w , and hence it maps the spherical region u 2 + υ 2 + w 2 ≤ 1 into the ellipsoidal region x 2 a 2 + y 2 b 2 + z 2 c 2 ≤ 1 In these exercises, perform the integration by transforming the ellipsoidal region of integration into a spherical region of integration and then evaluating the transformed integral in spherical coordinates. ∭ G x 2 d V , where G is the region enclosed by the ellipsoid 9 x 2 + 4 y 2 + z 2 = 36.
If a, b, and c are positive constants, then the transformation
x
=
a
u
,
y
=
b
υ
,
z
=
c
w
can be rewritten as
x
/
a
=
u
,
y
/
b
=
υ
,
z
/
c
=
w
,
and hence it maps the spherical region
u
2
+
υ
2
+
w
2
≤
1
into the ellipsoidal region
x
2
a
2
+
y
2
b
2
+
z
2
c
2
≤
1
In these exercises, perform the integration by transforming the ellipsoidal region of integration into a spherical region of integration and then evaluating the transformed integral in spherical coordinates.
∭
G
x
2
d
V
,
where G is the region enclosed by the ellipsoid
9
x
2
+
4
y
2
+
z
2
=
36.
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
Neat handwriting is perfectly acceptable. Please submit your assignment as ONE PDF file. Find the scalar equation of the plane containing both the line of intersection of the planes defined by ?1: 2x + 3y + z – 2 = 0 and ?2: x + 2y – z – 5 = 0 and the point P (1, 0, –2)
Determine all bilinear transformation which transform the half plane Re(z) >=0 into the unit circle |w|<=1.
Find parametric equations for the intersection of the planes 2x + y − 3z = 0 and x + y = 1
Precalculus: Mathematics for Calculus - 6th Edition
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