Evaluate the integral, where E is the region that lies inside the cylinder x2 + y2...
Use cylindrical coordinates. Evaluate SIS x2 + y2 dv, where E is the region that lies inside the cylinder x2 + y2 = 4 and between the planes z = 3 and z = 12. x
(1 point) Evaluate the triple integral I2(x2 +y2)dV where D is the region inside the parabolid z 4-x2-y2 and inside the first octant2 0, 0,z0 B. I 12 D. I E. I (1 point) Evaluate the triple integral I2(x2 +y2)dV where D is the region inside the parabolid z 4-x2-y2 and inside the first octant2 0, 0,z0 B. I 12 D. I E. I
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.
5. The solid E lies above the cone z = 3V x2 + y2, inside the cylinder x2 + y2 = 4 and below the plane z = 8; see Fig.2. (a) Write the equations of those three surfaces in cylindrical coordinates and say in which horizontal plane the cone intersects the cylinder. (b) Set up a triple iterated integral in cylindrical coordinates, for this triple integral SSI r’dV
Evaluate the triple integral I=∭D(x2+y2)dV where D is the region inside the cone z=x2+y2−−−−−−√, below the plane z=2 and inside the first octant x≥0,y≥0,z≥0. A. I=0 B. I=(π/20)2^5 C. I=(π/10)2^5 D. I=π2^5 E. I=(π/40)^25
Evaluate the triple integral. 3z dV, where E is bounded by the cylinder y2 + z2 = 9 and the planes x = 0, y = 3x, and z = 0 in the first octant E
All of 10 questions, please. 1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
Evaluate the following integral, ∫ ∫ S (x2 + y2 + z2) dS, where S is the part of the cylinder x2 + y2 = 25 between the planes z = 0 and z = 9, together with its top and bottom disks
10. Evaluate the given integral by changing to polar coordinates. JJR x2 + y2" where R is the region that lies between the circles x2 + y2 = a2 and x2 + y2 = 62 with 0 <a<b.
Evaluate the surface integral. 1. (x2+42+7) o ds S is the part of the cylinder x2 + y2 = 4 that lies between the planes z = 0 and 2 = 2, together with its top and bottom disks