Home
Class 12
MATHS
If m and n are positive integers and f(m...

If m and n are positive integers and `f(m,n)=int_(0)^(1)x^(n-1)(logx)^(m)dx`, then `f(m,n)` is equal to

A

`m/nf(m-1,n)`

B

`-m/nf(m-1,n)`

C

`n/mf(m-1,n)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    TARGET PUBLICATION|Exercise COMPETITIVE THINKING|148 Videos

  • CONTINUITY

    TARGET PUBLICATION|Exercise Evaluation Test|10 Videos

  • DIFFERENTIAL EQUATIONS

    TARGET PUBLICATION|Exercise EVALUATION TEST|25 Videos

Similar Questions

Explore conceptually related problems

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

If m and n are positive integers and f(x)=int_(1)^(x)(t-a)^(2n)(t-b)^(2m+1)dt,a!=b then

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

If n is a positive integer then int_(0)^(1)(ln x)^(n)dx is :

Given that sum_(k=1)^(35)sin5k^(@)=tan((m)/(n))^(@), where m and n are relatively prime positive integers that satisfy ((m)/(n))^(@)<90^(@), then m+n is equal to

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

If m , n are positive integers and m+nsqrt(2)=sqrt(41+24sqrt(2)) , then (m+n) is equal to

If m and n are positive integers such that (m-n)^(2)=(4mn)/((m+n-1)) , then how many pairs (m, n) are possible?

int(mx^(m+2n-1)-nx^(n-1))/(x^(2m+2n)+2x^(m+n)+1)dx is equal to

TARGET PUBLICATION-DEFINITE INTEGRALS-EVALUATIO TEST
  1. The value of the integral intalpha^beta 1/(sqrt((x-alpha)(beta-x)))dx

    Text Solution

    |

  2. Let f(x)=(e^(x)+1)/(e^(x)-1) and int(0)^(1) x^(3) .(e^(x)+1)/(e^(x)-1)...

    Text Solution

    |

  3. If m and n are positive integers and f(m,n)=int(0)^(1)x^(n-1)(logx)^(m...

    Text Solution

    |

  4. The least value of the function phi(x)=int((7pi)/6)^(x)(4sint+3cost)dt...

    Text Solution

    |

  5. Prove that int(a)^(b)f(x)dx=(b-a)int(0)^(1)f((b-a)x+a)dx

    Text Solution

    |

  6. The integral int0^(1. 5)[x^2]dx ,w h e r e[dot] denotoes the greatest ...

    Text Solution

    |

  7. If f(x) is a function satisfying f(1/x)+x^(2)f(x)=0 for all non zero x...

    Text Solution

    |

  8. lim(ntooo)1/n[1+sqrt(n/(n+1))+sqrt(n/(n+2))+sqrt(n/(n+3))+………..+sqrt(n...

    Text Solution

    |

  9. lim(n->oo)sum(n=1)^n(sqrt(n))/(sqrt(r)(3sqrt(r)+4sqrt(n))^2)

    Text Solution

    |

  10. Let f(x) be a function satisfyingf'(x)=f(x) withf(0) =1 and g(x) be a ...

    Text Solution

    |

  11. int(0)^(100pi)(|sin^(3)x|+|cos^(3)x|)dx=

    Text Solution

    |

  12. I1=int0^(pi/2)(sinx-cosx)/(1+sinxcosx)dx ,I2=int0^(2pi)cos^6xdx ,I3=in...

    Text Solution

    |

  13. overset(2pi) underset(0)int(xsin^(2n)x)/(sin^(2n)x+cos^(2n)x)dx,n gt 0...

    Text Solution

    |

  14. The equation int(-pi/4)^(pi/4){a|sinx|+(bsinx)/(1+cos^2x)+c}dx=0 where...

    Text Solution

    |

  15. int(0)^(sqrt("log"(pi)/2))cos(e^(x^(2)))2xe^(x^(2))dx=

    Text Solution

    |

  16. If f(x)=int(0)^(x)sin^(6)tdt, then f(x+pi)=

    Text Solution

    |

  17. If f(x) is a polynomial of degree 2, such that f(0)=3,f'(0)=-7,f''(0)=...

    Text Solution

    |

  18. If f(x)=Asin((pix)/2)+B, f'(1/2)=sqrt2 and int0^1 f(x)dx=(2A)/pi then ...

    Text Solution

    |

  19. If f(x)=|(sin x+sin x 2x+sin3x,sin2x,sin3x),(3+4sinx,3,4sinx),(1+sinx,...

    Text Solution

    |

  20. If a is a positive integer, then the number of values of a satisfying ...

    Text Solution

    |