Home
Class 12
MATHS
The value of I=int(pi//2)^(5pi//2)(e^(ta...

The value of `I=int(pi//2)^(5pi//2)(e^(tan^(-1)(sinx)))/(e^(tan^(-1)(sinx))+e^(tan^(-1)(cosx)))dx`, is

A

1

B

`pi`

C

e

D

`pi//2`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    MTG-WBJEE|Exercise WE JEE PREVIOUS YEARS QUESTIONS (CATEGORY 3 : ONE OR MORE THAN ONE OPTION CORRECT TYPE)|5 Videos
  • DEFINITE INTEGRALS

    MTG-WBJEE|Exercise WB JEE WORKOUT (CATEGORY 3 : ONE OR MORE THAN ONE OPTION CORRECT TYPE)|16 Videos
  • CONIC SECTIONS

    MTG-WBJEE|Exercise WB JEE PREVIOUS YEARS QUESTIONS (CATEGORY 3 : One or More than One Option Correct Type)|6 Videos
  • DERIVATIVES

    MTG-WBJEE|Exercise WB JEE PREVIOUS YEARS QUESTIONS|22 Videos

Similar Questions

Explore conceptually related problems

The value of the definite integral (1)/(pi)int_((pi)/(2))^((5 pi)/(2))(e^(tan^(-1)(sin x)))/(e^(tan^(-1)(sin x)+e^(tan^(-1)(cos x)))dx is )

If I=int_((pi)/(4))^((9pi)/(4))(e^(tan^(-1))(cosx))/(e^(tan^(-1))(sinx)+e^(tan^(-1))(cosx))dx then [I] is (where [.] denotes greatest integer function)

The value of int_(-pi//2)^(pi//2)(1)/(e^(sinx)+1) dx is equal to

int_(-pi//4)^(pi//4)(e^(x)(x^(3)sinx))/(e^(2x)-1)dx equals

Evaluate int_(pi/3)^(pi/2) e^x((1+sinx)/(1+cosx))dx

Evaluate: int_(-pi//2)^(pi//2)1/(1+e^(sinx))dx

(d)/(dx)[tan^(-1)((sinx)/(1+cosx))]=

Evaluate: int_0^(pi/2) (sin2x tan^(-1)(sinx))dx

int_(0)^(pi//2) sin 2x tan^(-1) (sinx)dx =

MTG-WBJEE-DEFINITE INTEGRALS-WE JEE PREVIOUS YEARS QUESTIONS (CATEGORY 2 : SINGLE OPTION CORRECT TYPE)
  1. Let f: RvecR be a continuous function which satisfies f(x)= int0^xf(t...

    Text Solution

    |

  2. lim(nrarroo)(sqrt1+sqrt2+…+sqrt(n-1))/(nsqrtn)=

    Text Solution

    |

  3. int0^1log(1/x-1)dx is equal to

    Text Solution

    |

  4. Estimate the absolute value of the integral int(10)^(19)(sinx)/(1+x^8)...

    Text Solution

    |

  5. L e tI1=int0^n[x]dxandI2=int0^n{x}dx ,where [x] and {x} are integral a...

    Text Solution

    |

  6. The value of the integral overset(1)underset(0)int e^(x^(2))dx lies in...

    Text Solution

    |

  7. int0^1000 e^(x-[x])dx

    Text Solution

    |

  8. If M=int(0)^((pi)/2)(cosx)/(x+2)dx and N=int(0)^((pi)/4)(sinxcosx)/((x...

    Text Solution

    |

  9. The value of the integral I = int(1//2014)^(2014)(tan^(-1) x)/x dx is

    Text Solution

    |

  10. Let I=int(pi//4)^(pi//3)(sinx)/(x)dx. Then

    Text Solution

    |

  11. The value of I=int(pi//2)^(5pi//2)(e^(tan^(-1)(sinx)))/(e^(tan^(-1)(si...

    Text Solution

    |

  12. The value of lim(nrarroo)(1)/(n)[sec^(2)""(pi)/(4n)+sec^(2)""(2pi)/(4n...

    Text Solution

    |

  13. The value of the integratio int(-pi//4)^(pi//4)(lambda|sinx|+(mu sinx)...

    Text Solution

    |

  14. lim(x->0) 1/x [int(y->a)e^(sin^2t) dt-int(x+y->a)e^(sin^2t)dt] is equa...

    Text Solution

    |

  15. The value of the integral int(-1)^(1){(x^(2015))/(e^(|x|)(x^(2)+cosx))...

    Text Solution

    |

  16. Let [a] denote the greatest integer which is less than or equal to a. ...

    Text Solution

    |

  17. The value of the integral int(pi//6)^(pi//2)((sinx-xcosx))/(x(x+sinx))...

    Text Solution

    |

  18. If [x] denotes the greatest integer less than or equal to x , then fin...

    Text Solution

    |

  19. If f(x)=int(-1)^(x)|t|dt, then for any x ge0,f(x) is equal to

    Text Solution

    |

  20. Evaluate: int0^(100pi)sqrt((1-cos2x))dxdot

    Text Solution

    |