Question 11 A solid in the first octant, bounded by the coordinate planes, the plane (x=...
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,...
1. Consider the solid in the first octant bounded by the coordinate planes, the plane x= 2,and the surface z= 9-y^2. The density is(x,y,z) = (x+ 1)(y+ 1)(z+ 1). Calculate the x,y, and z coordinates of the center of mass. Express your answer in decimal form. 2. Find Iz for the hollow cylinder (oriented along the z-axis) with inner radius R and thickness t. The base is the xy-plane, the height is h, and the density is(x,yz,) =kz^2.
please check your answer Question Details Let W be the solid in the first octant bounded by the top half of the cylinder x2 +z2= 36 and the plane x + y = 6 y Use Cartesian (rectangular) coordinates to set up the integral to find the volume of W in the order dydxdz. dy dz dx For instructor's notes only. Do not write in the box below. Question Details Let W be the solid in the first octant bounded...
please show complete work 25) Use a triple integral in the coordinate system of your choice to find the volume of the solid in the first octant bounded by the three planes y =0 z 0, and z 1-x x y2. Include a sketch of the solid as well as appropriate projection and an Hint: for rectangular coordinates, use dV might not be given in the exam dz dy dx. This hint 25) Use a triple integral in the coordinate...
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
Please try helping with all three questions.......please 1 point) Integratef(x, y, z) 6xz over the region in the first octant (x,y, z 0) above the parabolic cylinder z = y2 and below the paraboloid Answer Find the volume of the solid in R3 bounded by y-x2 , x-уг, z-x + y + 24, and Z-0. Consider the triple integral fsPw xyz2 dV, where W is the region bounded by Write the triple integral as an iterated integral in the order...
please solve 9 and extra credit: find the volume of the solid bounded by the three coordinate planes and the plane 6x + 8y + 2z - 24 = Problem 9. Find the largest possible volume of the rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane 3r +y+2z 12. Problem ro. Compute the integral (sncos y)drdy. Extra Problem. Find the volume of the solid bounded by the three coordinate...
Evaluate ∫∫∫T 2xy dx dy dz where T is the solid in the first octant bounded above by the cylinder z = 4 − x^2 below by the x, y-plane, and on the sides by the planes x =0, y = 2x and y = 4. Answer: ∫ (4, 0) ∫ (y/2, 0) ∫ (4−x^2, 0) 2xy dz dx dy = ∫ (2, 0) ∫ (4, 2x) ∫ (4−x^2, 0) 2xy dz dy dx = 128/3
6) Consider the solid region E bounded by x-0, x-2, 2-y, 2-y-1, 2-0, and 24, set up a triple integral and write it as an iterated integral in the indicated order of integration that represents the volume of the solid bounded by E. (Sometimes you need to use more than one integral.) (a) da dy dz (projecti (b) dy dz dr (projection on rz-plane) (c) dz dy dx (projection on ry-plane) (d) Calculate the volume of the solid E on...
Find the volume of the tetrahedron in the first octant bounded by the coordinate planes and the plane passing through (4,0,0), (0,3,0), and (0,0,5). (0.0.5) i (0,3,0) 4,0,0) The volume of the tetrahedron is . (Type an integer or a simplified fraction.)