In Problems 20 to 31, evaluate each integral in the simplest way possible. ∬ r ⋅ n d σ over the entire surface of the hemisphere x 2 + y 2 + z 2 = 9 , z ≥ 0 , where r = x i + y j + z k .
In Problems 20 to 31, evaluate each integral in the simplest way possible. ∬ r ⋅ n d σ over the entire surface of the hemisphere x 2 + y 2 + z 2 = 9 , z ≥ 0 , where r = x i + y j + z k .
In Problems 20 to 31, evaluate each integral in the simplest way possible.
∬
r
⋅
n
d
σ
over the entire surface of the hemisphere
x
2
+
y
2
+
z
2
=
9
,
z
≥
0
,
where
r
=
x
i
+
y
j
+
z
k
.
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.
Jo
18.9. Let y denote the boundary of the rectangle whose vertices are
-2 - 2i, 2 – 2i, 2+ i and -2+i in the positive direction. Evaluate each of
the following integrals:
(a).
COS Z
dz,
24
dz,
(2z +1)2
dz, (b).
T 2
4
(a).
dz
dz.
(0). LE (0.
sin z+
dz, (e). (z+1)
z2 +2
(22 + 3)2
Jutio inside and
10
5. Calculate each integral, assuming all circles are positively oriented:
· Sz²dz, where y is the line segment from 0 to -1+2i
a.
sin(22)dz
b. fc₂(41) 22²-81
$c₁ (74)
C.
e dz
22+49
z cos(z)dz
d. fc₂(3) (2-3)
Evaluate each of the following contour integrals:
(1) fc
sin z
22+7²
dz; z 2i = 2
-2
fc
e
sin z
z3
dz; |z1|= 3
1
3
-dz;
fc 2² (3² + 17d²; |2 — ²| = 2²/2
-
- i|
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