Home
Class 12
MATHS
If absalt1 show that int0^pi (log(1+acos...

If `absalt1` show that `int_0^pi (log(1+acosx))/cosx dx= pisin^(-1)a`

Promotional Banner

Topper's Solved these Questions

  • CONTINUITY & DIFFERENTIABILITY

    PATHFINDER|Exercise QUESTION BANK|13 Videos

  • DETERMINATES

    PATHFINDER|Exercise QUESTION BANK|21 Videos

Similar Questions

Explore conceptually related problems

Evaluate: int_0^pi log(1+cosx)dx

Find I=int_0^pi ln(1+cosx)dx

int _(0)^(pi/2) log(cotx)dx

Show that int_(0)^(1)(cos^(-1)x)^(2)dx=pi-2 .

The value of int_0^1 (8log(1+x))/(1+x^2) dx is

Show that : int_0^1(logx)/((1+x))dx=-int_0^1(log(1+x))/x dx

Evaluate : int_0^(pi/4)log(1+tanx)dx .

Evaluate int (dx)/(1+cosx)

Integrate : int log(sinx).cosx dx

PATHFINDER-DEFINITE INTEGRATION-QUESTION BANK
  1. Evaluate : int0^(pi//2) cos^3xcdot sinx dx

    Text Solution

    |

  2. Evaluate int0^(pi/4) (e^(secx) (sin(x+(pi/4)))/(cosx(1-sinx)) dx

    Text Solution

    |

  3. If absalt1 show that int0^pi (log(1+acosx))/cosx dx= pisin^(-1)a

    Text Solution

    |

  4. If Un=int0^pi (1-cosnx)/(1-cosx) dx where n is positive integer or zer...

    Text Solution

    |

  5. Prove that int0^x e^(xt)e^(-t^2)dt =e^(x^2/4) int0^xe^(-t^2/4)dt

    Text Solution

    |

  6. Find a function g:R rarr R continous in [0,infty] satisfying g(0) =1 a...

    Text Solution

    |

  7. Evaluate underset(nrarrinfty)lim 1/n overset(4n)underset(r=1)sum r/(sq...

    Text Solution

    |

  8. If In=int0^1 x^ntan^(-1)x dx then prove that (n+1)In +(n-1)I(n-2)=(pi/...

    Text Solution

    |

  9. If f(x)=x+int0^1(xy^2+x^2y) dy find f(x)

    Text Solution

    |

  10. The total number of distinct x in[0,1] for which int0^x t^2/(1+t^4) dt...

    Text Solution

    |

  11. The value of int(-pi/2)^(pi/2) (x^2cosx)/(1+e^x) dx is equal to

    Text Solution

    |

  12. underset(nrarrinfty)lim((n+1)(n+2)....3n)/(n^(2n)))^(1/n) is equal to

    Text Solution

    |

  13. int0^5 ((1/x)-1) dx= ?

    Text Solution

    |

  14. The value of underset(nrarrinfty)lim {(sqrt(n+1) +sqrt(n+2) +......+sq...

    Text Solution

    |

  15. if [x] denotes the greatest integer less than or equal to x then integ...

    Text Solution

    |

  16. (phi)t={1, for 0lelt1 0 otherwise then int(-3000)^(3000) (underset(r...

    Text Solution

    |

  17. Let f:RrarrR be a function defined by f(x)={([x],x,le,2),(0,x,gt,2):} ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |