multivariate calculus problem ..
SOS ... help
multivariate calculus problem .. SOS ... help Find the volume of a solid that lies under...
EXAMPLE 4 Find the volume of the solid that lies under the paraboloid z 5x2 - 5y2, above the xy-plane, and inside the cylinder x2 + y2-2x (x-1)2 + y2=1 or r 2 cos 8 SOLUTION The solid lies above the disk D whose boundary circle has equation x2 +y2x or, after completing the square, In polar coordinates we have x2 +y Thus the disk D is given by and x-r cos(), so the boundary circle becomes 2r cos(), or...
7. Find the volume of the solid region that lies under the surface 2 = ry and over the region in the xy plane bounded by the curves y = 2r and y = r A. 4/3 B. 8 C. 8/3 D. 32/3 E. none of the above 8. Evaluate SSSE Vx2 + y2 dV where E is the region bounded by the paraboloid z = x2 + y2 and the plane z = 4. A. 87 B. 327 c....
Problem 4. Find the volume of the solid that lies under the paraboloid 3 = x + y2 and above the region D in the ry-plane bounded by the line y = 2x and the parabola y = 1? Note: The region D is both of Type I and Type II.
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...
(1 point Find the volume of the solid that lies within the sphere x2 + 2 + z-64 above the xy plane, and outside the cone z 8V x2 y2 (1 point Find the volume of the solid that lies within the sphere x2 + 2 + z-64 above the xy plane, and outside the cone z 8V x2 y2
Find the volume of the solid that lies under the elliptic paraboloidx2/9 + y2/16 + z =1and above the rectangleR = [−1, 1] × [−3, 3].
Let E be the solid that lies inside the cylinder x^2 + y^2 = 1, above the xy-plane, and below the plane z = 1 + x. Let S be the surface that encloses E. Note that S consists of three sides: S1 is given by the cylinder x^2 + y^2 = 1, the bottom S2 is the disk x^2 + y^2 ≤ 1 in the plane z = 0, and the top S3 is part of the plane z...
Use spherical coordinates. Find the volume of the solid that lies within the sphere x2 + y2 + z2 = 4, above the xy-plane, and below the cone z =√( x2 + 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.
Use a triple integral to find the volume of the solid region inside the sphere ?2+?2+?2=6 and above the paraboloid ?=?2+?2 This question is in Thomas Calculus 14th edition chapter 15. Q2 // Use a triple integral to find the volume of the solid region inside the sphere x2 + y2 + z2 = 6 and above the paraboloid z = x2 + y2