In Problems 20 to 31, evaluate each integral in the simplest way possible. ∬ F ⋅ n d σ where F = y 2 − x 2 i + ( 2 x y − y ) j + 3 z k and σ is the entire surface of the tin can bounded by the cylinder x 2 + y 2 = 16 , z = 3 , z = − 3 .
In Problems 20 to 31, evaluate each integral in the simplest way possible. ∬ F ⋅ n d σ where F = y 2 − x 2 i + ( 2 x y − y ) j + 3 z k and σ is the entire surface of the tin can bounded by the cylinder x 2 + y 2 = 16 , z = 3 , z = − 3 .
In Problems 20 to 31, evaluate each integral in the simplest way possible.
∬
F
⋅
n
d
σ
where
F
=
y
2
−
x
2
i
+
(
2
x
y
−
y
)
j
+
3
z
k
and
σ
is the entire surface of the tin can bounded by the cylinder
x
2
+
y
2
=
16
,
z
=
3
,
z
=
−
3
.
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
Calculate the following integral
.2
Evaluate the line integral xy dx + x-dy, where C is the path going
counterclockwise around the boundary of the rectangle with corners (0,0),(2,0),(2,3),
and (0,3). You can evaluate directly or use Green's theorem. Write the integral(s), but
do not evaluate.
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