Set up, but do not evaluate, two different iterated integrals equal to the given integral. ∬ σ x 2 y d S , where σ is the portion of the cylinder y 2 + z 2 = a 2 in the first octant between the planes x = 0 , x = 9 , and z = 2 y .
Set up, but do not evaluate, two different iterated integrals equal to the given integral. ∬ σ x 2 y d S , where σ is the portion of the cylinder y 2 + z 2 = a 2 in the first octant between the planes x = 0 , x = 9 , and z = 2 y .
Set up, but do not evaluate, two different iterated integrals equal to the given integral.
∬
σ
x
2
y
d
S
,
where
σ
is the portion of the cylinder
y
2
+
z
2
=
a
2
in the first octant between the planes
x
=
0
,
x
=
9
,
and
z
=
2
y
.
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.
Evaluate the triple iterated integral.
T/2
r cos é dr de dz
Jo
10.Complete each part.
sin y
a.) Determine which of the following integrals is equal to |||
-dydx . Explain.
sin(y)
A.
drdy
В.
drdy
sin(y)
sin(y)
drdy
D.
drdy
b.) The coordinate plane 3x + 6y + 2z = 6 bounded by the
coordinate planes forms the solid shown at right. Which
formula would we integrate with respect to z and then y to
compute the volume? Explain.
3
A. 3-x-3y
2
В. 2-2у —
3
1
1
С. 1 —
D. 3r+6y+2z
-I-
3
c.) Which of these iterated integrals computes the area of the region shown? Explain.
А.
1 dydr
B.
dydr
(4,2)
1 dzdy
y = Vx
C.
D.
1 drdy
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