Home
Class 12
MATHS
Consider the integral "l"(1)=int(1)^(e)(...

Consider the integral `"l"_(1)=int_(1)^(e)(1+x)(x+Inx)^(100)dx. "l"_(2)=int_(sin^(-1)(1//e))^(pi//2) (1 + esinx + Insinx)^(101)cos x dx`
If `l_(1)+e/101 l_(2)=(e(1+e)^(101)-k)/101` then `kge`

A

0

B

1

C

2

D

`-1`

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
`I_(1)=int_(1)^(e)x ((1+x)/x)(x+In x)^(100) dx`
`=(e(e+1)^(101)-1)/101-1/101 int_(1)^(e)(x+Inx)^(101)dx`
`I_(2)=1/e int_(1)^(e)(t+Int)dt` on taking `e sin x=t`
`implies I_(1)+(eI_(2))/101=(e(e+1)^(101)-1)/101impliesK=1`
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINE

    FIITJEE|Exercise NUMERICAL BASED|4 Videos

  • TIPS

    FIITJEE|Exercise NUERICAL DECIMAL BASED QUATIONS|20 Videos

Similar Questions

Explore conceptually related problems

If I_(1)=int_(e)^(e^(2))(dx)/(ln x) and I_(2)=int_(1)^(2)(e^(x))/(x)dx

The integral I=int_(e)^(e+1)(1+x^(2))/(1+x^(3))dx satisfies

int_(0)^(1)e^(2x)e^(e^(x) dx =)

Evaluate the integrals int_(1)^(2)((1)/(x)-(1)/(2x^(2)))e^(2x)dx

int_(-1)^(1)e^(|x|)dx=2(e-1)

int_(0)^( pi/2)e^(x)((1+sin x)/(1+cos x))dx=

The value of the integral int_(-a)^(a)(e^(x))/(1+e^(x))dx is

If I_(1)=int_(e )^(e^(2)) (dx)/(logx)"and "I_(2)=int_(1)^(2)(e^(x))/(x)dx ,then

If l_(1)=int sin^(-1)x dx and l_(2) =int sin^(-1)sqrt(1-x^(2))dx , then

FIITJEE-TEST PAPERS-MATHEMATICS
  1. Let ABC be a triangle with incentre I. If P and Q are the feet of the ...

    Text Solution

    |

  2. Let hatu, hatv, hatw be three unit vectors such that hatu+hatv+hatw=ha...

    Text Solution

    |

  3. Consider the integral "l"(1)=int(1)^(e)(1+x)(x+Inx)^(100)dx. "l"(2)=in...

    Text Solution

    |

  4. The equation k+x^(3)e^(x+3)=0 has 2 distinct real roots & k is a prime...

    Text Solution

    |

  5. If the equation2^((2pi)/cos^(-1)x)-(a+1/2)2^((pi)/cos^(-1)x-a^2=0 has ...

    Text Solution

    |

  6. Equation of the circles |z-1-i|=1 & |z-1+i|=1 touches internally a cir...

    Text Solution

    |

  7. Let a=sin^(-)(sin3)+sin^(-1)(sin4)+sin^(-1)(sin5),f(x)=e^(x^(2)+|x|), ...

    Text Solution

    |

  8. A tosses 2 fair coins & B tosses 3 fair cons after game is won by the ...

    Text Solution

    |

  9. The vertices of a triangle OBC are O(0,0),B(-3,-1),C(-1,-3). Equation ...

    Text Solution

    |

  10. 8 Children are standing in a line outside a ticket counter at zoo. 4 o...

    Text Solution

    |

  11. In a triangle ABC, /ABC=45^@ and a point D is on BC such that 2BD=CD a...

    Text Solution

    |

  12. Let n be a positive integer if 1le1gt K len such that (sin^(2)nx)/(sin...

    Text Solution

    |

  13. Given A={f:C[0,1]:int(0)^(1)f(x)dx=1} then minimum value of int(0)^(1)...

    Text Solution

    |

  14. Straight line 3x-4y=4/(pi)sin^(-1)(a^(8)+1)+2cos^(-1)(a^(12)+1)-sec^(-...

    Text Solution

    |

  15. If f(x) be a twice differentiable function from RR rarr RR such that t...

    Text Solution

    |

  16. If the sides a, b & c /\ABC is such that a/(1+alpha^(2)beta^(2))=b/(al...

    Text Solution

    |

  17. If A1 is the area area bounded by |x-ai| + |y|=bi, i in N ,where a(i...

    Text Solution

    |

  18. bara & barb be two vectors such that |a|=1,|b|=4& bara.barb=2. If barc...

    Text Solution

    |

  19. f(x)is defined for xge0 & has a continuous derivative. It satisfies f(...

    Text Solution

    |

  20. If bara & barb are any two unit vectors then possible integers in the ...

    Text Solution

    |