Use spherical coordinates to evaluate the triple integral
∭e^−(x^2+y^2+z^2)/(x^2 + y^2 + z^2) dV , Where...
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
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
1A) Use surface integral to evaluate the flux
of
F(x,y,z) =<x^3,y^3,z^3>
across the cylinder x^2+y^2=1, 0<=z<=2
1B) Use the Divergence Theorem to evaluate the
flux of F(x,y,z) =<x^3,y^3,z^3>
across the cylinder x^2+y^2=1, 0<=z<=2
Use the Stoke’s theorem to evaluate Z Z S (∇×F)·nˆ·dS where F(x,
y, z) = (x^2 z^2,y^2 z^2, xyz) and surface S is part of the
paraboloid z = x^2 + y^2 that lies inside the cylinder x^2 + y^2 =
4, oriented upwards. Sketch the surface S and label everything.
Use spherical coordinates to find the volume of solid within the
sphere x^2 + y^2 + z^2 = 16 and above the cone 3z^2 = x^2 + y^2 and
lying in the 1st octant.
using / for integral
Evaluate the double integral //R cos( (y-x)/(y+x) )dA where R is
the trapezoidal region with vertices (1,0), (2,0), (0,2), and
(0,1)
Evaluate the line integral, where C is the given curve.
∫CF(x,y,z)⋅dr where F(x,y,z)=xi+yj+ysin(z+1)k and C
consists of the line segment from (2,4,-1) to (1,-1,3).