Home
Class 12
MATHS
If alpha=int0^1(e^(9x+3tan^(-1)x))((12+9...

If `alpha=int_0^1(e^(9x+3tan^(-1)x))((12+9x^2)/(1+x^2))dx` where `tan^(-1)x` takes only principal values, then, find the value of `((log)_e|1+alpha|-(3pi)/4)`

Text Solution

Verified by Experts

The correct Answer is:
9
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise Exercise 3 Part - II|25 Videos

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise High Level Problem|26 Videos

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise Exercise 2 Part - IV|6 Videos

  • COMBINATORICS

    RESONANCE ENGLISH|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|5 Videos

  • DPP

    RESONANCE ENGLISH|Exercise QUESTION|656 Videos

Similar Questions

Explore conceptually related problems

int e^(tan^(-1)x) ((1+x+x^2)/(1+x^2))dx

Evaluate: int(e^tan^(-1)(x))/(1+x^2)\ dx

The value of int_(0)^(1) tan^(-1)((2x-1)/(1+x-x^(2)))dx is

Find the value of int_(0)^(2pi)1/(1+tan^(4)x)dx

int_0^(pi/2)1/(1+tan^2x)dx

int((1+x+x^(2))/( 1+x^(2))) e^(tan^(-1)x) dx is equal to

If cos^(-1).(6x)/(1 + 9x^(2)) = -(pi)/(2) + 2 tan^(-1) 3x , then find the values of x

If tan^(-1)((x-1)/(x-2))+tan^(-1)((x+1)/(x+2))=pi/4 , then find the value of x .

Evaluate: int_(-1)^3(tan^(-1)(x/(x^2+1))+tan^(-1)((x^2+1)/x))dx

Evaluate int_(log1//3)^(log3)tan((e^(x)-1)/(e^(x)+1))dx

RESONANCE ENGLISH-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 3 Part - I
  1. ((int(-1/2)^(1/2)cos 2x *log((1+x)/(1-x))dx))/((int(0)^(1/2)cos 2x *lo...

    Text Solution

    |

  2. Let f: RvecR be a function defined by f(x)={[x],(xlt=2) \ \ (0,x >2) ...

    Text Solution

    |

  3. If alpha=int0^1(e^(9x+3tan^(-1)x))((12+9x^2)/(1+x^2))dx where tan^(-1)...

    Text Solution

    |

  4. Let f: R rarr R be a continuous odd function, which vanishes exactly a...

    Text Solution

    |

  5. Let f(x)=7tan^8x+7tan^6x-3tan^4x-3tan^2x for all x in (-pi/2,pi/2) . ...

    Text Solution

    |

  6. Let f'(x)=(192x^(3))/(2+sin^(4)pix) for all x epsilonR with f(1/2)=0. ...

    Text Solution

    |

  7. The option(s) with the values of aa n dL that satisfy the following eq...

    Text Solution

    |

  8. Let F:RtoR be a thrice differntiable function. Suppose that F(1)=0,F(3...

    Text Solution

    |

  9. Let F : R to R be a thrice differentiable function . Suppose that F(...

    Text Solution

    |

  10. Let F(x)=intx^[x^2+pi/6](2cos^2t)dt for all x in R and f:[0,1/2] -> [0...

    Text Solution

    |

  11. The total number for distinct x epsilon[0,1] for which int(0)^(x)(t^(2...

    Text Solution

    |

  12. Evaluate: int(-pi//2)^(pi//2)(x^2cosx)/(1+e^x)dx

    Text Solution

    |

  13. Area of the region {(x,y) in R^(2):ygesqrt(|x+3|),5ylex+9le15} is eq...

    Text Solution

    |

  14. Let f:Rto(0,1) be a continuous function. Then, which of the following ...

    Text Solution

    |

  15. Let f: R -> R be a differentiable function such that f(0) = 0,f(pi/2)=...

    Text Solution

    |

  16. If Isum(k=1)^(98)intk^(k+1)(k+1)/(x(x+1))dx ,t h e n: (a) I<(49)/(50...

    Text Solution

    |

  17. If the line x = alpha divides the area of region R = {(x,y) in R^(2) :...

    Text Solution

    |

  18. If g(x)=int(sinx)^("sin"(2x))sin^(-1)(t)dt ,t h e n : (a) g^(prime)(...

    Text Solution

    |

  19. For each positive integer n let y(n)=1/n((n+1)(n+2)…..(n+n)^(1//n))....

    Text Solution

    |

  20. A farmer F(1) has a land in the shape of a triangle with vertices at P...

    Text Solution

    |