Verify Formula (1) in the Divergence Theorem by evaluating the surface integral and the triple integral. F x , y , z = 5j + 7 k ; σ is the sphere x 2 + y 2 + z 2 = 1.
Verify Formula (1) in the Divergence Theorem by evaluating the surface integral and the triple integral. F x , y , z = 5j + 7 k ; σ is the sphere x 2 + y 2 + z 2 = 1.
Verify Formula (1) in the Divergence Theorem by evaluating the surface integral and the triple integral.
F
x
,
y
,
z
=
5j
+
7
k
;
σ
is the sphere
x
2
+
y
2
+
z
2
=
1.
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.
6. Use the Stokes theorem to evaluate f Fdr where F
(3x – 2y +32) i +(4x – 2y+32) 5 + (2x –
3y | 22) k and C is the circle: æ = 3, y? | 22 = 4, oricnted counterclockwisc when vicwcd from the
positive part of x-axis. Describe the surface S whose boundary is C and state its orientation.
Find the area of the surface, which is part of the surface z = 1 + 3x + 2y2 that lies above the triangle with vertices (0, 0), (0, 1) and (2, 1).
Verify Stokes' theorem where A = (x-z)i + (x³ +zy)j-3x y²k and S is the
surface of z=2-√√x² + y² above xy-plane.
evaluate
whe
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