Use a CAS to find the value of the surface integral ∬ σ x 2 y z d S where the surface σ is the portion of the elliptic paraboloid z = 5 − 3 x 2 − 2 y 2 that lies above the x y -plane .
Use a CAS to find the value of the surface integral ∬ σ x 2 y z d S where the surface σ is the portion of the elliptic paraboloid z = 5 − 3 x 2 − 2 y 2 that lies above the x y -plane .
Use a CAS to find the value of the surface integral
∬
σ
x
2
y
z
d
S
where the surface
σ
is the portion of the elliptic paraboloid
z
=
5
−
3
x
2
−
2
y
2
that lies above the
x
y
-plane
.
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.
Find the area of the surface x2 - 2y - 2z = 0 that lies above the triangle bounded by the lines x = 2, y = 0, and y = 3x in the xy-plane.
Find the area of the surface cut out from the bottom of the paraboloid z = x² + y² by the plane z = 20.
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.
University Calculus: Early Transcendentals (3rd Edition)
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