Home
Class 12
MATHS
Evaluate: 5050(int0 1(1-x^(50))^(100)dx)...

Evaluate: `5050(int0 1(1-x^(50))^(100)dx)/(int0 1(1-x^(50))^(101)dx)`

Text Solution

Verified by Experts

The correct Answer is:
5051
`int_(0)^(1)(1-x^(50))^(101)dx`
`=[x(1-x^(50))^(101)]_(0)^(1)-int_(0)^(1)x.101(1-x^(50))^(100)(-50x^(49))dx`
`=0+5050 int_(0)^(1)x^(50)(1-x^(50))^(100)dx`
`=-5050int_(0)^(1)(1-x^(50)-1)(1-x^(50))^(100)dx`
`=-5050int_(0)^(1)(1-x^(50))^(101)dx+5050int_(0)^(1)(1-x^(50))^(100)dx`
`=5051int_(0)^(1)(1-x^(50))^(101)dx=5050int_(0)^(1)(1-x^(50))^(100) dx`
`implies 5050(int_(0)^(1)(1-x^(50))^(100)dx)/((1-x^(50))^(101)dx)=5051`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    CENGAGE|Exercise JEE Main Previous Year|12 Videos

  • DEFINITE INTEGRATION

    CENGAGE|Exercise JEE Advanced Previous Year|38 Videos

  • DEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Matrix)|6 Videos

  • CURVE TRACING

    CENGAGE|Exercise Exercise|24 Videos

  • DETERMINANT

    CENGAGE|Exercise Multiple Correct Answer|5 Videos

Similar Questions

Explore conceptually related problems

Find the value of (5050int0 1(1-x^(50))^(100)dx)/(int0 1(1-x^(50))^(100)dx)

Evaluate: 5050(int_(0)^(1)(1-x^(50))^(100)dx)/(int_(0)^(1)(1-x^(50))^(101)dx)

The value of ((5050)int_(0)^(1)(1-x^(50))^(100)dx)/(int_(0)^(1)(1-x^(50))^(101)dx) is

The vlaue of ((5050)int_(0)^(1)(1-x^(50))^(100)dx)/(int_(0)^(1) (1-x^(50))^(100)dx) , is

Evaluate: int_0^1x(1-x)^n dx

If I_(1)=int_(0)^(1)(1-x^(50))^(100)dx and I_(2)=int_(0)^(1)(1-x^(50))^(101)dx, If I_(2)=(alpha)/(beta)I_(1) ( alpha,beta are coprime) then beta-alpha

Find the value of (29int_(0)^(1)(1-x^(4))^(7)dx)/(4int_(0)^(1)(1-x^(4))^(6))dx

Evaluate int_0^1 (1/x)(1-x^3)^(-1/2) dx

Evaluate int_0^2 |1-x| dx

CENGAGE-DEFINITE INTEGRATION -Exercise (Numerical)
  1. The value of int(0)^(1)(tan^(-1)x)/(cot^(-1)(1-x+x^(2))dx is.

    Text Solution

    |

  2. Let f(x) be differentiate function symmetric about x=2, then the value...

    Text Solution

    |

  3. Let f:[0,oo)vecR be a continuous strictly increasing function, such th...

    Text Solution

    |

  4. If f is continuous function and F(x)=int0^x((2t+3)dotintt^2f(u)d u)dt ...

    Text Solution

    |

  5. If the value of the definite integral int0^1(sin^(-1)sqrt(x))/(x^2-x+1...

    Text Solution

    |

  6. Let f(x)=int(0)^(x)(dt)/(sqrt(1+t^(3))) and g(x) be the inverse of f(x...

    Text Solution

    |

  7. Let g(x) be differentiable on R and int(sint)^1x^2g(x)dx=(1-sint), wh...

    Text Solution

    |

  8. If int0^oox^(2n+1)dote^(-xdx)=360 , then the value of n is

    Text Solution

    |

  9. Let f(x) be a derivable function satisfying f(x)=int0^x e^tsin(x-t)dt...

    Text Solution

    |

  10. Let f(x)=1/x^2 int0^x (4t^2-2f'(t))dt then find 9f'(4)

    Text Solution

    |

  11. If the value of the definite integral int0^1^(2007)C7x^(2000)dot(1-x)^...

    Text Solution

    |

  12. IfIn=int0^1(1-x^5)^n dx ,t h e n(55)/7(I(10))/(I(11))i se q u a lto

    Text Solution

    |

  13. Evaluate: 5050(int0 1(1-x^(50))^(100)dx)/(int0 1(1-x^(50))^(101)dx)

    Text Solution

    |

  14. L e tJ=int(-5)^(-4)(3-x^2)tan(3-x^2)dxa n dK=int(-2)^(-1)(6-6x+x^2) t...

    Text Solution

    |

  15. The value of the definite integral int(2-1)^(sqrt(2)+1)(x^4+x^2+2)/((x...

    Text Solution

    |

  16. Consider a real valued continuous function f such that f(x)=sinx + int...

    Text Solution

    |

  17. Iff(x)=x+int0^1t(x+t)f(t)dt ,t h e nt h ev a l u eof(23)/2f(0) is ...

    Text Solution

    |

  18. Let y=f(x)=4x^(3)+2x-6, then the value of int(0)^(2)f(x)dx+int(0)^(30)...

    Text Solution

    |

  19. The value of int(1)^(3)(sqrt(1+(x-1)^(3))+(x^(2)-1)^(1/3)+1)dx is .

    Text Solution

    |

  20. The value of int(0)^(1)cos^(-1)(x-x^(2))-sqrt((1-x^(2))(2x-x^(2)))dx i...

    Text Solution

    |