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4. (9-22 - y2)dV where H is the solid hemisphere ? + 4. Evaluate SS y2...
Use spherical coordinates.
Evaluate
(4 − x2 − y2) dV, where H is
the solid hemisphere x2 + y2 + z2
≤ 16, z ≥ 0.
H
mmer 2019 3. Evaluate: M y2 dV where E the solid hemisphere x2 + y2 +z2 9 and y 2 0 indrnse)
mmer 2019 3. Evaluate: M y2 dV where E the solid hemisphere x2 + y2 +z2 9 and y 2 0 indrnse)
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...
Q4. Evaluate SS (3x – 2y) dv, where is the region between the sphere x2 + y2 + z2 = 1 and x2 + y2 + z2 = 4 with z so. (Hints. Use Spherical Coordinate system)
JJJE Evaluate the triple integral (2 + xy) dV, where is the solid region above the paraboloid z = 22 + y2 and below the plane z = 9. O 817 O 547 O 1627 O 1087 O 727
Evaluate Sl] (z2 + y2 + 22)-1/2 av je D where D is the solid between the spheres 22 + y2 + 2 = 14 and 22 + y2 + 2 = 19 (Note: Remember to type pi for . Also keep fractions, for example write 1/2 not 0.5.) 11/ 62+72+27-14 + y2 + 22)-1/2 dv=
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.
4. (15 pts) Evaluate I = SSSR (x2 + y2 + z²) dV where R is the cylinder given by 4 < x2 + y2 +z? 59.
er 20 / Quiz 9 Remaining Time: 138:14 Evaluate 8 +y2 +22)-1/2 av where D is the solid between the spheres 22 + y2 + 2 = 20 and 2 + y2 + 2 – 34 (Note: Remember to type pi for. Also keep fractions, for example write 1/2 not 0.5.) IS + y2 +22)-1/2 dv= D Submit Assignment Quit & Save Back Question M O 4x ENG
(1) Let P denote the solid bounded by the surface of the hemisphere zV1--y2 and the cone z-Vx2 + y2 and let n denote an outwardly directed unit normal vector. Define the vector field (a) Evaluate the surface integral F nds directly without using Gauss' Divergence T heorem (b) Evaluate thetriplengral IIdiv(F) dV directly without using Gauss Diver- gence Theorem. confirming the result of Gauss' Divergence Theorem for this particular example.
(1) Let P denote the solid bounded by the...