2. Find the volume of the solid in the first octant (simultaneously) below the surfaces z = 2y 2 + 1, z = 4 − x, and z = 4 − y.
2. Find the volume of the solid in the first octant (simultaneously) below the surfaces z = 2y 2 ...
Find the volume of the solid in the first octant bounded by the parabolic cylinder z = 4 - x2 and the plane y = 4.
Find the volume of the solid in the first octant bounded by the parabolic cylinder z = 25 − x2 and the plane y = 2.
Find the volume of the solid in the first octant bounded by the parabolic cylinder z = 16 ? x2 and the plane y = 2.
Find the volume of the solid in the first octant that is enclosed by the graphs z=1-y2 , x+y=1 and x+y=3. Sketch. -> USING Z-SIMPLE <- *** NOT using x-simple. ***
Find the volume of the given solid region in the first octant bounded by the plane 2x + 2y + 4z4 and the coordinate planes, using triple integrals 0.0(020 Complete the triple integral below used to find the volume of the given solid region. Note the order of integration dz dy dx. dz dy dx Use a triple integral to find the volume of the solid bounded by the surfaces z-2e and z 2 over the rectangle (x.y): 0 sxs1,...
oi o 2. Find the area of the part of the paraboloidty that is cut off by the plane -4 3. Find volume of the solid in the first octant bounded by y 2r and the plane r-4 3. Find volume of the solid in the first octant bounded by y= 2x, and 4. Find the volume of the solid bounded above by the spherex2+y+ 4. Find the volume of the solid bounded above by the sphere+y?+ 2 9, below...
3. Find the volume of the solid in the first octant that lies above the cone z = 13(x+ + y) and inside the sphere x2 + y2 + y2 = 42. Use spherical coordinates. 4. Determine if the vectorfield F(x, y) - (x + y)i + (2xy + y) is conservative If it is, find a potential function
3. Find the volume of the solid in the first octant that lies above the cone z = 3(x + y) and inside the sphere x2 + y2 + z2 = 42. Use spherical coordinates.
Find the mass of thc solid region bounded by the parabolic surfaces z - 16- 2r2-2y and 2x2 + 2y2 if the density of the solid at the point (x, y, z) is δ(z, y, z) = Vz? + y2
Find the mass of thc solid region bounded by the parabolic surfaces z - 16- 2r2-2y and 2x2 + 2y2 if the density of the solid at the point (x, y, z) is δ(z, y, z) = Vz? + y2
SET UP a triple integral to find the volume of the solid in the
first octant (all coordinates positive) that is below the pla
10. (8 pts.) SET UP a triple integral to find the volume of the solid in the first octant (all coordinates positive) that is below the plane x+3y + 2z =12.