Can you please solve q4? ThanksAlso, provide detailed answer. In this project we find formulas for the volume enclosed by a hypersphere in n-dimensionalspace.1. Use a double integral and trigonometric substitution, together with the formula11Scosu du =-u+÷sin(2u)+C from the Table of Integrals, to find the area of a circle with radius r.42. Use a triple integral and trigonometric substitution to find the volume of a sphere with radius r.3. Use a quadruple integral to find the hypervolume enclosed by the hypersphere inx² + y² +z? + w² = r? in R* . (Use only trigonometric substitution and the reduction formulas forSsin" x- dx or fcos" x•dx .)4. Use an n-tuple integral to find the volume enclosed by a hypersphere of radius r in n-dimensional spaceR". [Hint: The formulas are different for n even and n odd.]

Name: Can you please solve q4? ThanksAlso, provide detailed answer. In this
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Description: Can you please solve q4? ThanksAlso, provide detailed answer. In this project we find formulas for the volume enclosed by a hypersphere in n-dimensionalspace.1. Use a double integral and trigonometric substitution, together with the formula11Scosu du

Answered: 4. Use an n-tuple integral to find the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Can you please solve q4? Thanks

Also, provide detailed answer.

In this project we find formulas for the volume enclosed by a hypersphere in n-dimensional
space.
1. Use a double integral and trigonometric substitution, together with the formula
1
1
Scos
u du =-u+÷sin(2u)+C from the Table of Integrals, to find the area of a circle with radius r.
4
2. Use a triple integral and trigonometric substitution to find the volume of a sphere with radius r.
3. Use a quadruple integral to find the hypervolume enclosed by the hypersphere in
x² + y² +z? + w² = r? in R* . (Use only trigonometric substitution and the reduction formulas for
Ssin" x- dx or fcos" x•dx .)
4. Use an n-tuple integral to find the volume enclosed by a hypersphere of radius r in n-dimensional space
R". [Hint: The formulas are different for n even and n odd.]

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1. Use a double integral and trigonometric substitution, together with the formula
1
1
[cos²u du ==u+
u+ sin(2u)+C from the Table of Integrals, to find the area of a circle with radius r.
2
2. Use a triple integral and trigonometric substitution to find the volume of a sphere with radius r.

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