Set up the integral to find the volume of the tetrahedron bounded by the planes x...
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 GETTING YOUR BOUNDS.
Homework Answers
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Set up the integral to find the volume of the tetrahedron
bounded by the planes x...
Find the volume of the tetrahedron bounded by the planes x + 2y + z = 2, x = 2y, x = 0 and z = 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.
Use double integrals to calculate the volume of the tetrahedron bounded by the coordinate planes (x= 0, y = 0, z = 0) a...
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,...
Use a triple integral to find the volume of the given solid.The tetrahedron enclosed by...
Use a triple integral to find the volume of the given solid.The tetrahedron enclosed by the coordinate planes and the plane
5x + y + z =
3Evaluate the triple integral.8z dV, where E is
bounded by the cylinder y2 +z2 = 9 and the planes x = 0,y = 3x, and z = 0 in the first
octantEUse a triple integral to find the volume of the given solid. The tetrahedron enclosed by the coordinate planes and the plane...
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 f...
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. Let E be the tetrahedron bounded by the planes 2x +2y +2=6,1 = 0, y...
10. Let E be the tetrahedron bounded by the planes 2x +2y +2=6,1 = 0, y = 0, and 2 = 0. Express the following integral as an iterated double integral. Do not evaluate. SIS 6.ry dy
2. (13 points) Let E be the solid region bounded by the planes x = 0,...
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.
Find the volume (or set up integral) of the solid obtained by rotating the region bounded...
Find the volume (or set up integral) of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region and a typical disk/washer or shell (depending on the method used). Use the method indicated if given, otherwise you choose the method. As indicated, either calculate the integral to find the volume (yes) or just set up the integral - limits of integration included - that you would use to calculate the volume,...
Triple Integration Problems. 1. Integrate zdV JJ w where ll' is enclosed by the planes z = 0 and cylinders x2 + y2 4 and x2 + y,: 9 = x+9+ 3 and by the 2. Integrate where E is bounded by the zu-pl...
Triple Integration
Problems.
1. Integrate zdV JJ w where ll' is enclosed by the planes z = 0 and cylinders x2 + y2 4 and x2 + y,: 9 = x+9+ 3 and by the 2. Integrate where E is bounded by the zu-plane and the hemispheres z/9-2y2 and z = V/10-22-27 Change the order of integration and evaluate x3 sin(уз)dydx. 0 Jr2
1. Integrate zdV JJ w where ll' is enclosed by the planes z = 0 and cylinders...
Question 11 A solid in the first octant, bounded by the coordinate planes, the plane (x=...
Question 11 A solid in the first octant, bounded by the coordinate planes, the plane (x= a) and the curve (z=1-y). Find the volume of the solid by using : #-Double integration technique (Use order dy dx) a=51 b-Triple integration technique (Use order dz dy dx) ..
Use a triple integral to find the volume of the given solid. The solid bounded by...
Use a triple integral to find the volume of the given solid. The solid bounded by the parabolic cylinder y = x2 and the planes z = 0, z = 10, y = 16.Evaluate the triple integral. \iiintE 21 y zcos (4 x⁵) d V, where E={(x, y, z) | 0 ≤ x ≤ 1,0 ≤ y ≤ x, x ≤ z ≤ 2 x}Find the volume of the given solid. Enclosed by the paraboloid z = 2x2 + 4y2 and...
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,...
Use a triple integral to find the volume of the given solid.The tetrahedron enclosed by the coordinate planes and the plane
5x + y + z =
3Evaluate the triple integral.8z dV, where E is
bounded by the cylinder y2 +z2 = 9 and the planes x = 0,y = 3x, and z = 0 in the first
octantEUse a triple integral to find the volume of the given solid. The tetrahedron enclosed by the coordinate planes and the plane...
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. Let E be the tetrahedron bounded by the planes 2x +2y +2=6,1 = 0, y = 0, and 2 = 0. Express the following integral as an iterated double integral. Do not evaluate. SIS 6.ry dy
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.
Find the volume (or set up integral) of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region and a typical disk/washer or shell (depending on the method used). Use the method indicated if given, otherwise you choose the method. As indicated, either calculate the integral to find the volume (yes) or just set up the integral - limits of integration included - that you would use to calculate the volume,...
Triple Integration
Problems.
1. Integrate zdV JJ w where ll' is enclosed by the planes z = 0 and cylinders x2 + y2 4 and x2 + y,: 9 = x+9+ 3 and by the 2. Integrate where E is bounded by the zu-plane and the hemispheres z/9-2y2 and z = V/10-22-27 Change the order of integration and evaluate x3 sin(уз)dydx. 0 Jr2
1. Integrate zdV JJ w where ll' is enclosed by the planes z = 0 and cylinders...
Question 11 A solid in the first octant, bounded by the coordinate planes, the plane (x= a) and the curve (z=1-y). Find the volume of the solid by using : #-Double integration technique (Use order dy dx) a=51 b-Triple integration technique (Use order dz dy dx) ..
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