Use spherical coordinates to evaluate the triple integral
∭e^−(x^2+y^2+z^2)/(x^2 + y^2 + z^2) dV , Where E is the region
bounded by the spheres x^2 + y^2 + z^2 = 4 and x^2 + y^2 + z^2 =
9
Evaluate the following integral,
∫
∫
S
(x2 + y2 + z2) dS,
where S is the part of the cylinder x2 +
y2 = 64 between the planes z = 0 and
z = 7, together with its top and bottom disks.
Set up the triple integral of an arbitrary continuous function
f(x, y, z) in spherical coordinates over the solid shown. (Assume a
= 4 and b = 8. ) f(x, y, z) dV E = 0 π/2 f , , dρ dθ dφ 4
2. Assume that the potential in Cartesian coordinates is given
as V=x2-y2. According to this;
(a) The value of the potential at coordinate P (2, -1,3)
(b) Electric field, the magnitude of the displacement vector and
field lines
(c) Calculate the charge density on the conductive surface
Curvilinear integral of the function f (x, y) = x2 +
y2 on a (3,0) centered and 3 radius circle.
a)Calculate the curvilinear integral by expressing the curve in
parametrically.
b)Calculate the curvilinear integral by expressing the curve in
polar coordinates.
c)Calculate the curvilinear integral by expressing the curve in
cartesian coordinates.