Answer #2 without using matrix :Directions: Solve the following problems NEATLY, COMPLETELY and CORRECTLY. Youmust submit the problem set through Canvas in PDF file. Do NOT use graphing devices in yourwork.1.Identify the surfaces of the following equations by converting them intoequations in the Cartesian form. Show your complete solutions.(a) ² = 4 + 4r²(b) psin osin2.Evaluate the double integral that will find the volume of a solid bounded by==1-2y²-3² and the zy- plane.(Hint: Use trigonometric substitution to evaluate the formulated double integral.)3Set-up the iterated double integral in polar coordinates that gives the volumeof the solid enclosed by the hyperboloid = √√/1++ and under the plane z = 5.4.Evaluate the double integral:CLAdr dy.(Hint: Change the order of integration to dy dr.)5Use Cartesian coordinates to evaluatey²dVwhere D is the tetrahedron in the first octant bounded by the coordinate planes and theplane 2r +3y+z=6. Use dV= dz dy dr. Draw the solid D.6.Set up the triple integral that will give the following:(a) the volume of R using cylindrical coordinates with dV= r dz dr de where R:0≤z≤ 1,0 ≤ y ≤ √1-7²,0 ≤ ≤ √√√4=(2²+ y2). Draw the solid R.(b) the volume of the solid B that lies above the cone: = √32²+3y² and below thesphere ² + y² +22= using spherical coordinates. Draw the solid B

Answered: Image /qna-images/answer/4aed8d72-808e-4bd9-8050-240783ac335e.jpg

Answered: Evaluate the double integral that will…

Evaluate the double integral that will find the volume of a solid bounded by = = 1-2y²-3r² and the zy- plane. (Hint: Use trigonometric substitution to evaluate the formulated double integral.)

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter10: Analytic Geometry

Section10.1: The Rectangular Coordinate System

Problem 40E: Find the exact volume of the solid that results when the region bounded in quadrant I by the axes...

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Question

Answer #2 without using matrix

:
Directions: Solve the following problems NEATLY, COMPLETELY and CORRECTLY. You
must submit the problem set through Canvas in PDF file. Do NOT use graphing devices in your
work.
1.
Identify the surfaces of the following equations by converting them into
equations in the Cartesian form. Show your complete solutions.
(a) ² = 4 + 4r²
(b) psin osin
2.
Evaluate the double integral that will find the volume of a solid bounded by
==1-2y²-3² and the zy- plane.
(Hint: Use trigonometric substitution to evaluate the formulated double integral.)
3
Set-up the iterated double integral in polar coordinates that gives the volume
of the solid enclosed by the hyperboloid = √√/1++ and under the plane z = 5.
4.
Evaluate the double integral:
CLA
dr dy.
(Hint: Change the order of integration to dy dr.)
5
Use Cartesian coordinates to evaluate
y²dV
where D is the tetrahedron in the first octant bounded by the coordinate planes and the
plane 2r +3y+z=6. Use dV= dz dy dr. Draw the solid D.
6.
Set up the triple integral that will give the following:
(a) the volume of R using cylindrical coordinates with dV= r dz dr de where R:0≤
z≤ 1,0 ≤ y ≤ √1-7²,0 ≤ ≤ √√√4=(2²+ y2). Draw the solid R.
(b) the volume of the solid B that lies above the cone: = √32²+3y² and below the
sphere ² + y² +22= using spherical coordinates. Draw the solid B

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