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.
2. Evatuate the following Complex Integration:
2-i
(a) Evaluate
| (3xy + iy?) dz along the straight line joining z = i and z = 2 .
(b) Evaluate
dz, where C is the circle |z – 2| = ;.
22 – 3z + 2
Answer 3
8.
Determine whether each integral is
comvergent
are conivergent
or dive
ergent. Evalua te those othat
Evaluàte othat
thoue
a s x-i dx
X-1 dx
X4
b) J (i+x) Ji+x3 dx
+x? dx
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
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