33. Using beta function evaluate the following integrals: (i) So x² (1 – x)² dx; (ii) S0" x³ (100 – x)" dx; (iii) ſ x'1 (1 – x³)" dx.
33. Using beta function evaluate the following integrals: (i) So x² (1 – x)² dx; (ii) S0" x³ (100 – x)" dx; (iii) ſ x'1 (1 – x³)" dx.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![The beta distribution involves the notion of beta function. First we
explain the notion of the beta integral and some of its simple properties. Let
a and B be any two positive real numbers. The beta function B(a, B) is
defined as
1
B(a, ß) = | xª-1(1 – x)8-'dx.
3–1
First, we prove a theorem that establishes the connection between the
beta function and the gamma function.
Theorem 6.4. Let a and ß be any two positive real numbers. Then
B(a, B):
Г(а)Г(3)
T(a + B) '](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff7da3d53-31d2-48e7-b787-228d47eca939%2F70c540c2-fa08-425f-b06d-8a04dc51e9a7%2Fb5t2iph_processed.png&w=3840&q=75)
Transcribed Image Text:The beta distribution involves the notion of beta function. First we
explain the notion of the beta integral and some of its simple properties. Let
a and B be any two positive real numbers. The beta function B(a, B) is
defined as
1
B(a, ß) = | xª-1(1 – x)8-'dx.
3–1
First, we prove a theorem that establishes the connection between the
beta function and the gamma function.
Theorem 6.4. Let a and ß be any two positive real numbers. Then
B(a, B):
Г(а)Г(3)
T(a + B) '
![33. Using beta function evaluate the following integrals:
(i) S x² (1 – x)² dæ; (ii) S,00 æ³ (100 – æ)* dx; (iii) x11 (1 – a*)7 dx.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff7da3d53-31d2-48e7-b787-228d47eca939%2F70c540c2-fa08-425f-b06d-8a04dc51e9a7%2F9lxsll_processed.png&w=3840&q=75)
Transcribed Image Text:33. Using beta function evaluate the following integrals:
(i) S x² (1 – x)² dæ; (ii) S,00 æ³ (100 – æ)* dx; (iii) x11 (1 – a*)7 dx.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)