6. (15) By evaluation of the volume integral find the volume of the region bounded by...
11. Use the triple integral to find the volume for the region bounded by y = 0, y=1-22 , and sitting above z = y2 – 3?, sitting below 2 = y.
Find the volume of the region in the first octant bounded by the coordinate planes , the plane y+z=3, and the cylinder x=9-y2
4. (14 points) Using polar coordinates, set up, but DO NOT EVALUATE, a double integral to find the volume of the solid region inside the cylinder x2 +(y-1)2-1 bounded above by the surface z=e-/-/ and bounded below by the xy-plane.
4. (14 points) Using polar coordinates, set up, but DO NOT EVALUATE, a double integral to find the volume of the solid region inside the cylinder x2 +(y-1)2-1 bounded above by the surface z=e-/-/ and bounded below by the xy-plane.
1 point) Find the volume of the wedge-shaped region (Figure 1) contained in the cylinder x2 + y2-4 and bounded above by the plane z = x and below by the xy-plane. z=x FIGURE 1
1 point) Find the volume of the wedge-shaped region (Figure 1) contained in the cylinder x2 + y2-4 and bounded above by the plane z = x and below by the xy-plane. z=x FIGURE 1
(a) Find the volume of the region bounded above by the sphere x2 +y2 +z225 and below by the plane z - 4 by using cylindrical coordinates Evaluate the integral (b) 2x2dA ER where R is the region bounded by the square - 2
11. Evaluate S. 'S*(1 + 3x2 + 2y?) dx dy. 12. Find the volume in the first octant of the solid bounded by the cylinder y2 + z2 = 4 and the plane x = 2y. Graph for Problem 12 13. Find the volume under the paraboloid z = 4 - x2 - y2 and above the xy-plane. N Consider the solid region bounded above by the sphere x + y + z = 8 and bounded below by the...
11. [-/1 Points] DETAILS MY NOTES Find the volume of the region between the graph of f(x, y) = 81 – x2 - y2 and the xy plane. Submit Answer 12. [-/1 Points] DETAILS MY NOTES Find the volume of an ice cream cone bounded by the hemisphere z = V 50 - x2 y2 and the cone z = V + y2.
2. Set up and evaluate the volume integral for the region whose base D lies in the first quadrant in the xy plane and whose top is bounded by x + y + z = 4. 3. Find the volume that is enclosed by both the cone z = x2 + y2 and the sphere x2 + y2 + z = 2
(1 point) Evaluate the triple integral redV where E is the region bounded by the parabolic cylinder z 1-y2 and the planesz = 0, x = i, and x =-1.
(1 point) Evaluate the triple integral redV where E is the region bounded by the parabolic cylinder z 1-y2 and the planesz = 0, x = i, and x =-1.
5. Use a triple integral to find the volume of the region Q bounded by the graphs of: z- 4y2, z 2, x 0, x 2. [Assume distance in meters
5. Use a triple integral to find the volume of the region Q bounded by the graphs of: z- 4y2, z 2, x 0, x 2. [Assume distance in meters