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.]

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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…

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Advanced Math

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.]

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter65: Achievement Review—section Six

Section: Chapter Questions

Problem 52AR

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Statistics is the study of data collection, organization, analysis, interpretation, and presentation. Statistical bias is a characteristic of a statistical technique or its findings in which the expected value deviates from the actual root quantitative parameter being estimated. According to the actual definition of bias, it refers to the tendency of a statistic to overestimate or underestimate a parameter.

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Question

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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