Can you answer exercise no. 1? Example 2. Find the solid above the xy - plane bounded by the elliptic paraboloid z = x2+ 4y² and the cylinder x2 + 4y2 = 4.Solution. The z limit are 0 to x² + 4y². The y limits for -of the volume are from 0 to -V4 - x². The x limits for the first octantare from 0 to 2. We evaluate the triple integral by an iterated integral and obtainVa- x22V4-x²2+4y²v=S§ *** dzdydx = f o (x² + 4y²)dydx2V =4-x4y3- S [z*y + dx%3D= + 2) V4 – x-dx=--(4 – x²)3/2 + 2xV4 – x² + 8sin= 4mExercise. Solve.1. Use a triple integral to find the volume of the solid the tetrahedron enclosed by 2x +y+z =4 and the coordinateplanes.

Given data: The tetrahedron is enclosed by plane 2x+y+z=4 and coordinate planes.

Answered: 1. Use a triple integral to find the…

1. Use a triple integral to find the volume of the solid the tetrahedron enclosed by 2x + y+ z 4 and the coordinate planes.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 12T

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Question

Can you answer exercise no. 1?

Example 2. Find the solid above the xy - plane bounded by the elliptic paraboloid z = x2+ 4y² and the cylinder x2 + 4y2 = 4.
Solution. The z limit are 0 to x² + 4y². The y limits for -of the volume are from 0 to -V4 - x². The x limits for the first octant
are from 0 to 2. We evaluate the triple integral by an iterated integral and obtain
Va- x2
2
V4-x²
2+4y²
v=S§ *** dzdydx = f o (x² + 4y²)dydx
2
V =
4-x
4y3
- S [z*y + dx
%3D
= + 2) V4 – x-dx
=--(4 – x²)3/2 + 2xV4 – x² + 8sin
= 4m
Exercise. Solve.
1. Use a triple integral to find the volume of the solid the tetrahedron enclosed by 2x +y+z =4 and the coordinate
planes.

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