Home
Class 12
MATHS
The value of integral int(0)^(log5)(e^(x...

The value of integral `int_(0)^(log5)(e^(x)sqrt(e^(x)-1))/(e^(x)+3)dx` is

A

`3+2pi`

B

`4-pi`

C

`2+pi`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Putting `e^(x)-1=t^(2)` in the given integral, we have
`I=overset(log5)underset(0)int (e^(x)sqrt(e^(x)-1))/(e^(x)+3)dx=2 overset(2)underset(0)int (t^(2))/(t^(2)+4)dt=2{overset(2)underset(0)int 1"dt"-4overset(2)underset(0)int("dt")/(t^(2)+4}}`
`rArr I=2[t-2tan^(-1)((t)/(2))]_(0)^(2)=2[2-2xx(pi)/(4)]=4-pi`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

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

  • DEFINITE INTEGRALS

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

  • CONTINUITY AND DIFFERENTIABILITY

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|87 Videos

  • DERIVATIVE AS A RATE MEASURER

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|26 Videos

Similar Questions

Explore conceptually related problems

The value of the integral int_0^(log5)(e^xsqrt(e^x-1))/(e^x+3)dx

int_(0)^(log 2)(e^(x))/(1+e^(x))dx=

The value of integral int_(1)^(e) (log x)^(3)dx , is

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

int_(0)^(1)(dx)/(e^(x)+e^(-x))

Find the value of integral A=int_(-a)^(a)(e^(x))/(1+ e^x)dx

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

int_(0)^(1) (dx)/(e^(x)+e^(-x))

Evaluate : int_(0)^(1)(e^(sqrt(x)))/(sqrt(x))dx

The value of int_(log1//2)^(log2)sin{(e^(x)-1)/(e^(x)+1)}dx is equal to

OBJECTIVE RD SHARMA ENGLISH-DEFINITE INTEGRALS-Chapter Test 2
  1. The value of integral int(0)^(log5)(e^(x)sqrt(e^(x)-1))/(e^(x)+3)dx is

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  4. Let f (x) be a function satisfying f(x)=f(x) with f(0) = 1 and g be th...

    Text Solution

    |

  5. If I=int(0)^(1)cos(2 cot^(-1)sqrt(((1-x)/(1+x))))dx then :

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  10. Evaluate int(0)^(1)log(sin((pix)/(2)))dx

    Text Solution

    |

  11. Evaluate int(0)^(pi) xlog sinx dx

    Text Solution

    |

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

    Text Solution

    |

  13. If f(x)={{:(x,xlt1),(x-1,xge1):}, then underset(0)overset(2)intx^(2)f(...

    Text Solution

    |

  14. The value of the integral overset(1)underset(0)int (1)/((1+x^(2))^(3//...

    Text Solution

    |

  15. Prove that: int0^(2a)f(x)dx=int0^(2a)f(2a-x)dxdot

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  20. The value of alpha in [0,2pi] which does not satify the equation int(p...

    Text Solution

    |

  21. lim(x to 0)(int(0)^(x^(2))sinsqrt(t) dt)/(x^(3)) is equl to

    Text Solution

    |