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10. Let E be the tetrahedron bounded by the planes 2x +2y +2=6,1 = 0, y...
Let R be the tetrahedron bounded by the planes x = 0, y = 0, : = 0 and 6x+5y+ 92 = 4. The volume of R is given by Calculate the values of the following: a b= C de fo g A two-dimensional lamina occupies the triangle bounded by the lines r = 0, y = 4 1 and 3 3+ 4y = 6. The lamina has density function of p=9x² +5. The mass of the plate is given...
4. Let E be a solid bounded by the following planes: r = 0, y=0,2 = 0, z = 6-y, z = 8-T; see Fig.1. This solid is a region in the space of I, II and III type. Express SSS f(, y, z)dV by means of a triple iterated integral, which corresponds to the fact that E is of type II and next by means of a triple iterated integral, which corresponds to the fact that E is of...
Use double integrals to calculate the volume of the tetrahedron bounded by the coordinate planes (x= 0, y = 0, z = 0) and the plane 7x + 5y +z-35 0. Find the double integral needed to determine the volume of the region. Set up the inner integral with respect to y, and the outer integral with respect to x. Use double integrals to calculate the volume of the tetrahedron bounded by the coordinate planes (x= 0, y = 0,...
Find the volume of the tetrahedron bounded by the planes x + 2y + z = 2, x = 2y, x = 0 and z = 0 . Sketch the diagram of the tetrahedron with labeled points with coordinate axes and the boundary equations.
2. (13 points) Let E be the solid region bounded by the planes x = 0, y = 0, 2=0, and x+y+z=1. (a) Sketch E. (b) Set up the integral SSSe ex+y+z dV as a triple iterated integral. (c) Compute the integral.
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...
Set up the integral to find the volume of the tetrahedron bounded by the planes x + 2y + z = 8, x = 2y, x = 0, and z = 0, using a: a) double integral with order dydx. b) double integral with order dxdy. c) triple integral with any order of integration. YOUR WORK SHOULD INCLUDE A SKETCH OF THE REGION YOU ARE INTEGRATING OVER AND A CLEAR DESCRIPTION (CAN USE THE PICTURE HERE) OF HOW YOU ARE...
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,...
10) Calculate the integral zdac dy dz where D is bounded by the planes x = - 0, y = 0, z = 0, z = 1, and the cylinder x2 + y2 = 1 with x > 0 and y> 0. 11) Let y be the boundary of the rectangle with sides x = 1, y = 2, x = 3 and y = 3. Use Green's theorem to evaluate the following integral 2y + sina 1+2 1 +...
7. Let R be the quadrilateral bounded by the lines: y-2x = 0, y --23 = -9, 2y - x = 0, and 2y - = 4. Set up, but do not compute, the following integral with the given change of variables | || (34 – 30) da, u= »–20, y = 2y