Home
Class 12
MATHS
Compute the integral I(m,n) = int(0)^(1)...

Compute the integral `I_(m,n) = int_(0)^(1) x^(m) (! - x)^(n) ` dx , where m and n are non-negative integers.

Text Solution

Verified by Experts

The correct Answer is:
`I_(m,n) = (m!n!)/((m + n + 1)!)`
Promotional Banner

Topper's Solved these Questions

  • THE DEFINITE INTEGRAL

    IA MARON|Exercise 6 . 7 (Approximating Definite Integrals)|5 Videos

  • THE DEFINITE INTEGRAL

    IA MARON|Exercise 6 . 8 (Additional Problems)|3 Videos

  • THE DEFINITE INTEGRAL

    IA MARON|Exercise 6. 5 (Simplification of Integrals Based on the Properties of Symmetry of Integrands)|14 Videos

  • INTRODUCTION OF MATHEMATICAL ANALYSIS

    IA MARON|Exercise Additional Problems|34 Videos

Similar Questions

Explore conceptually related problems

If I(m,n)=int_(0)^(1)x^(m-1)(1-x)^(n-1)dx, then

If I_(m,n)= int_(0)^(1) x^(m) (ln x)^(n) dx then I_(m,n) is also equal to

Consider the integral I_(m) = int_(0)^(pi) (sin2mx)/(sinx ) dx , where m is a positive integer. What is I_(m) equal to ?

Consider the integral I_(m) = int_(0)^(pi) (sin2mx)/(sinx ) dx , where m is a positive integer. What is I_(1) equal to ?

If m, n in N , then l_(m n) = int_(0)^(1) x^(m) (1-x)^(n) dx is equal to

IA MARON-THE DEFINITE INTEGRAL -6 . 6 (Integration by Parts. Reduction Formulas)
  1. Compute the integral int (1)^(0) I n ^(3) x dx

    Text Solution

    |

  2. Compute the integral int(0)^(pi^(2)/4) sin sqrt(x) dx

    Text Solution

    |

  3. Compute the integral I = int(0)^(1) ("arc sin x")/(sqrt(1 - x^(2)))dx

    Text Solution

    |

  4. int(0)^(pi//2) x^(2) sin x " " dx=

    Text Solution

    |

  5. Compute the integral I(n) = int(0)^(a) (a^(2) - x^(2))^(n) dx , where...

    Text Solution

    |

  6. Using the result of the preceding problem obtain the following formula...

    Text Solution

    |

  7. Compute the integral H(m) = int(0)^(pi//2) sin^(m) x dx = int(0)^(p...

    Text Solution

    |

  8. Compute the integral I = int(0)^(x) x sin^(m) x dx (m is natur...

    Text Solution

    |

  9. Compute the integral I (n) = int(0)^(1) x^(m) (I n x)^(n) dx , m gt 0,...

    Text Solution

    |

  10. Compute the integral I(m,n) = int(0)^(1) x^(m) (! - x)^(n) dx , where...

    Text Solution

    |

  11. Compute the integrals : int(0)^(1) " arc tan " sqrt(x) dx

    Text Solution

    |

  12. Compute the integrals : int (x - 1)e^(-x) dx

    Text Solution

    |

  13. Compute the integrals : int(pi//4)^(pi//3) (x dx)/( sin^(2) x)

    Text Solution

    |

  14. Compute the integrals : int(0)^(1) x "arc tan x dx

    Text Solution

    |

  15. Compute the integrals : int(0)^(1) x I n (1 + x^(2)) dx

    Text Solution

    |

  16. int(0)^(pi//4) log (1+tan x) dx =?

    Text Solution

    |

  17. Compute the integrals : int (0) ^(pi//2) " sin In 2 x arc tan " ...

    Text Solution

    |

  18. Compute the integrals : int(1) ^(15) "arc tan " sqrt(sqrt(x) - 1)...

    Text Solution

    |

  19. Prove that int(0)^(1) ("arc cosx")^(n) dx = n ((pi)/(2))^(n-1) - n ...

    Text Solution

    |

  20. Prove that if f'' is continuous on [a,b] then the following formula...

    Text Solution

    |