4. (20 points) Use integration in spherical coordinates to evaluate the triple integral where E i...
5. In spherical coordinates evaluate the triple integral [ff (x2 + y2 +z?)2dV where D is the unit ball. (20 points)
4. Using spherical coordinates, evaluate the triple integral: ry: dl, where E lies between the spheres r2+94:2-4 and r2+92+ะ2-16 and above the cone V+v) or Recommend separating! 5. Using spherical coordinates, find the volume of the solid that lies within the sphere r2+y2+2 9, above the ry-plane, and below the cone ะ-V/r2 + y2 Reconnnend separating! 6. Using spherical coordinates, evaluate the triple integral: 2 + dV where E is the portion of the solid ball 2+2+2 s 4 that...
(1 point) Use spherical coordinates to evaluate the triple integral dV, e-(x+y+z) E Vx2 + y2 + z2 where E is the region bounded by the spheres x² + y2 + z2 = 4 and x² + y2 + z2 16. Answer =
Use cylindrical coordinates to evaluate the triple integral ∭E √(x2+y2)dV where E is the solid bounded by the circular paraboloid z = 1-1(x2+y2) and the xy -plane.
Use spherical coordinates to calculate the triple integral of fx, y, z) over the given region. rx, y, z) = ρ; x2 + y2 + Z2 16, 2.52, x20 Use spherical coordinates to calculate the triple integral of fx, y, z) over the given region. rx, y, z) = ρ; x2 + y2 + Z2 16, 2.52, x20
Use spherical coordinates to calculate the triple integral of f(x, y, z) = y over the region x2 + y2 + z2 < 3, x, y, z < 0. (Use symbolic notation and fractions where needed.) S S lw y DV = help (fractions)
Suppose you have to use spherical coordinates to evaluate the triple integral SI z dV where D is the solid region that lies inside the cone z = 22 + y2 and inside the sphere 22 + y2 +22 = 144 D Then the triple ingral in terms of spherical coordinates is given by Select all that apply p3 cos • sin o dp do do D [!] > av = 6*6** ? [!] > av = 6"* )*S" So*%*%**...
A) solve this integral in cylindrical coordinates. b) set up the integral in spherical coordinates (without solving) 10 points Compute the following triple integral: 1/ 1.32 + plav JD where D is the region given by V x2 + y2 <2<2. Hint: z= V x2 + y2 is a cone.
1. (13 pts.) Use spherical coordinates to set up the triple integral for the solid that is constructed from a portion of a sphere, x2 +y2 +Z2-1 that lies above the cone φ = π/4 . Do NOT evaluate. 1. (13 pts.) Use spherical coordinates to set up the triple integral for the solid that is constructed from a portion of a sphere, x2 +y2 +Z2-1 that lies above the cone φ = π/4 . Do NOT evaluate.
Suppose you have to use spherical coordinates to evaluate the triple integral III z av where D is the solid region that lies inside the cone z = /22 + y2 and inside the sphere 22 + y2 + 2 = 121 D Then the triple ingral in terms of spherical coordinates is given by Select all that apply pcos o dp do de z dV = cos sin o dp do de D z DV = D pocos o...