Home
Class 12
MATHS
If (m,m) =int(0)^(1)t^(m)(1-t)^(n)dt, th...

If (m,m) `=int_(0)^(1)t^(m)(1-t)^(n)dt`, then the expression for I(m,n) in terms of I (m+1,n-1), is

A

`(2^(n))/(m+1)-(n)/(m+1)I(m+1,n-1)`

B

`(n)/(m+1)I(m+1,n-1)`

C

`(2^(n))/(m+1)-(n)/(m+1)I(m+1,n-1)`

D

`(m)/(n+1)I(m+1,n-1)`

Text Solution

Verified by Experts

The correct Answer is:
B
We have,
`I(m,n)-overset(1)underset(0)intt^(m)(1-t)^(n)dt`
`rArr 1(m+1,n-1)=overset(1)underset(0)int t^(m+1)(1-t)^(n-1)dt`
`rArr I(m+1,n-1)=[-(t^(m+1)(1-t)^(n))/(n)]_(0)^(1)+(m+1)/(n)underset(0)overset(1)int t^(m)(1-t)^(n)dt`
`rArr 1(m+1,n-1)=(m+1)/(n)I(m,n)`
`rArr (m,n)=(n)/(m+1)I(m+1,n-1)`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA|Exercise Section I - Solved Mcqs|145 Videos

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA|Exercise Section II - Assertion Reason Type|12 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    OBJECTIVE RD SHARMA|Exercise Exercise|86 Videos

  • DERIVATIVE AS A RATE MEASURER

    OBJECTIVE RD SHARMA|Exercise Exercise|26 Videos

Similar Questions

Explore conceptually related problems

If I(m,n)=int_(0)^(1)t^(m)(1+t)^(n).dt, then the expression for I(m,n) in terms of I(m+1,n-1) is:

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

If L(m,n)=int_(0)^(1)t^(m)(1+t)^(n),dt , then prove that L(m,n)=(2^(n))/(m+1)-n/(m+1)L(m+1,n-1)

If I(m,n)=int_(0)^(1)x^(m-1)(1-x)^(n-1)dx,(m,n in I,m,n>=0),th epsilonI(m,n)=int_(0)^(oo)(x^(m-1))/((1+x)^(m-n))dxI(m,n)=int_(0)^(oo)(x^(m-1))/((1+x)^(m+n))dxI(m,n)=int_(0)^(oo)(x^(n-1))/((1+x)^(m+n))dxI(m,n)=int_(0)^(oo)(x^(n))/((1+x)^(m+n))dx

int_(0)^(1)x^((m-1))(1-x)^((n-1))dx is equal to where m,n in N

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

OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Chapter Test 2
  1. If (m,m) =int(0)^(1)t^(m)(1-t)^(n)dt, then the expression for I(m,n) i...

    Text Solution

    |

  2. The integral int(0)^(r pi) sin^(2x)x dx is equal to

    Text Solution

    |

  3. The value of the integral int(0)^(2)x[x]dx

    Text Solution

    |

  4. The value of integral sum (k=1)^(n) int (0)^(1) f(k - 1+x) dx is

    Text Solution

    |

  5. Let f(x) be a funntion satifying f'(x)=f(x) with f(0)=1 and g(x) be th...

    Text Solution

    |

  6. If I=int(0)^(1) cos{ 2 "cot"^(-1)sqrt((1-x)/(1+x))}dx then

    Text Solution

    |

  7. The value of int(a)^(a+(pi//2))(sin^(4)x+cos^(4)x)dx is

    Text Solution

    |

  8. The vaue of int(-1)^(2) (|x|)/(x)dx is

    Text Solution

    |

  9. The value of int0^1 (x^(3))/(1+x^(8))dx is

    Text Solution

    |

  10. The value of int(0)^(3) xsqrt(1+x)dx, is

    Text Solution

    |

  11. The value of the integral int(0)^(1) log sin ((pix)/(2))dx is

    Text Solution

    |

  12. The value of the integral int(0)^(pi)x log sin x dx is

    Text Solution

    |

  13. If I(1)=int(0)^(oo) (dx)/(1+x^(4))dx and I(2)underset(0)overset(oo)in...

    Text Solution

    |

  14. If f(x)={{:(x,"for " x lt 1),(x-1,"for " x ge1):},"then" int(0)^(2) x...

    Text Solution

    |

  15. The value of the integral int(0)^(2) (1)/((x^(2)+1)^(3//2))dx is

    Text Solution

    |

  16. If int(0)^(2a) f(x)dx=int(0)^(2a) f(x)dx, then

    Text Solution

    |

  17. If int(0)^(36) (1)/(2x+9)dx =log k, is equal to

    Text Solution

    |

  18. The value of the integral int(0)^(pi//2) sin^(6) x dx, is

    Text Solution

    |

  19. If int(0)^(oo) e^(-x^(2))dx=sqrt((pi)/(2))"then"int(0)^(oo) e^(-ax^(2)...

    Text Solution

    |

  20. The value of the integral int 0^oo 1/(1+x^4)dx is

    Text Solution

    |

  21. If int(pi//2)^(x) sqrt(3-2sin^(2)u) dx+int(dx)^(dy) equal pi//2

    Text Solution

    |