3. Use spherical coordinates to evaluate the integral V dV where is the portion of the...
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...
dV, where is the unit ball in R3, that is, Use spherical coordinates to compute the integral We E = {(x, y, z)| 22 + y2 + 2 <1}.
Evaluate the following integral in spherical coordinates. SSS--(=y2 +22)3120v 3/2 dV; D is a ball of radius 5 D SSS - (x2 + y2 +22) >/?dv=E D (Type an exact answer, using a as needed.)
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*%*%**...
(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 =
1. Use cylindrical coordinates to SET UP the integral for the volume of the portion of the unit ball, 22 +232 + x2 < 1, above the plane z = 12 2. (a) Write in spherical coordinates the equations of the following surfaces: (i) x2 + y2 + x2 = 4 (ii) z = 3x2 + 3y2 (b) SET UP the integral in spherical coordinates for the volume of the solid inside the surface 22 + y2 + x2 =...
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...
3. Use spherical coordinates: a) Evaluate IILr2 + ข้า dV where E is the solid region inside the sphere 12 + y2 + ~2-16 and above the cone 3r2 + 3y2 b) Find the centroid of the solid hemisphere of radius a, centered at the origin and lying above the xy- plane 3. Use spherical coordinates: a) Evaluate IILr2 + ข้า dV where E is the solid region inside the sphere 12 + y2 + ~2-16 and above the cone...
ago 2. Evaluate Is ver **av where Eis the 2. Evaluate ++"dV where E is the portion of the unit ball x² + y2 +z? 51 lying in the first octant (x,y,z 20).
Use spherical coordinates. Evaluate (4 − x2 − y2) dV, where H is the solid hemisphere x2 + y2 + z2 ≤ 16, z ≥ 0. H