please answer question 3. 1. Find the integral of the function f(x, y, z)xy+2 z over the region enclosed by the planex +y+z 2 2. Find the volume and center of gravity for the solid in the first octant (x 20, y 20, z20) bounded by 3. Find the center of mass for the solid hemisphere centered at the origin with radius a if the density and the coordinate planes z0,y 0, and x0 the parabolic ellipsoid Z-4-r-y. function is...
1. Find the volume of the solid under the cone z= sqrt (x^2 + y^2) and over the ring 4 |\eq x^2 + y^2 |\eq 25. 2. Find the volume of the solid under the plane 6x + 4y + z= 12 and over the disk with border x^2 + y^2 = y. 3. The area of the smallest region, locked by the spiral r\Theta= 1, the circles r=1 and r=3 and the polar axis.
Set up the triple integral of an arbitrary continuous function f(x, y, z) in cylindrical or spherical coordinates over each solid shown & described below. i.e., Fill in the six limits of integration and the blank at the end. There is nothing to evaluate. (a) The solid is between the top hemisphere of the ball of radius 2 centered at the origin and the inside of the upper half cone z = Vx2 + y2. r?+ y2 + = 4...
Please help with these. I have no idea how to do them. For problems 1-7, find the volume of the solid formed by rotating the region bounded by the given curves about the indicated axis. 4. y = x1, x = 0, y = 1 (in the first quadrant); about the y-axis 6. y = -x - 2 + 2, y = 0; about the x-axis 8. Find the volume of the frustum of a right circular cone with height...
(1 point) Find the volume of the solid that lies within the sphere x2 +y2 .2 16, above the xy plane, and outside the cone 2 (1 point) Find the volume of the solid that lies within the sphere x2 +y2 .2 16, above the xy plane, and outside the cone 2
Use a change of variables to find the volume of the solid region lying below the surface -f(x, y) and above the plane region R x, y)xy)e- R: region bounded by the square with vertices (4, 0), (6, 2), (4, 4), (2, 2) Use a change of variables to find the volume of the solid region lying below the surface -f(x, y) and above the plane region R x, y)xy)e- R: region bounded by the square with vertices (4, 0),...
Problem 2 (1) Find the area enclosed by the curves y 2 and y-4z-z2 (2) Find the volume of the solid whose base is the triangular region with vertices(0, 0), (2, 0), and (0,1). Cross-sections perpendicular to the y-axis semicircles. are (3) Find the volume of the solid by rotating the region bounded by y=1-z2 and y-0 about the r-axis. 2-z2. Find the volume (4) Let R be the region bounded by y--x2 and y of the solid obtained by...
plane, and outside the cone z-5V x2 (1 point Find the volume of the solid that lies within the sphere x2 ,2 + z2-25, above the x (1 point) Find the mass of the triangular region with vertices (0,0), (1, 0), and (0, 5), with density function ρ (x,y) = x2 +y. plane, and outside the cone z-5V x2 (1 point Find the volume of the solid that lies within the sphere x2 ,2 + z2-25, above the x (1...
(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
1. Using polar coordinates in the x-y plane, find the volume of the solid above the cone z r and below the hemisphere z= v8-r2. As a check the answer is approximately 13.88 but of course you have to calculate the exact answer 2. At the right is the graph of the 8-leafed rose r 1+2cos(40) Calculate the area of the small leaf. As a check the answer is 0.136 to 3 places of decimal (But of course you have...