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
2. Sketch the cylinder
y = x² +1.
4. A parabolic plate, shown below, is submerged in water.
2 m
|
3 m
If the top of the plate is 1m below the water's surface, set – up the definite
integral to find the force on the plate.
Probability and Statistics for Engineers and Scientists
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.