Home
Class 12
MATHS
Show that (a) int(e)^(e^(2))(1)/(log x)d...

Show that (a) `int_(e)^(e^(2))(1)/(log x)dx = int_(1)^(2)(e^(x))/(x)dx`
(b) `int_(t)^(1)(dx)/(1+x^(2)) = int_(1)^(1//t)(dx)/(1+x^(2))`

Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    AAKASH SERIES|Exercise Exercise - 2.7 (Level-2)|21 Videos

  • COMPLEX NUMBERS

    AAKASH SERIES|Exercise PRACTICE EXERCISE|93 Videos

  • DEMOIVRE'S THEOREM

    AAKASH SERIES|Exercise PRACTICE EXERCISE|64 Videos

Similar Questions

Explore conceptually related problems

Show that int_(e)^(e^(2))(1)/(log x) dx = int_(1)^(2)(e^(x))/(x) dx

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

int(x+1)^(2)e^(x)dx=

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

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

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

If int_(0)^(b)(dx)/(1+x^(2))=int_(b)^(oo)(dx)/(1+x_(2)), then b=

int_(1)^(e)((logx)^(3))/(x)dx=

AAKASH SERIES-DEFINITE INTEGRALS-Exercise (Level-2)
  1. Show that int(0)^(1//2)(x sin^(-1)x)/(sqrt(1-x^(2)))dx = (1)/(2)-(sqrt...

    Text Solution

    |

  2. Prove that int(0)^(pi//2) tan^(-1)(sin x) .sin 2x = (pi)/(2)-1

    Text Solution

    |

  3. Show that (a) int(e)^(e^(2))(1)/(log x)dx = int(1)^(2)(e^(x))/(x)dx ...

    Text Solution

    |

  4. Prove that int(0)^(1) log(sqrt(1-x)+sqrt(1+x))dx = (1)/(2) log 2 + (pi...

    Text Solution

    |

  5. Show that int(0)^(pi//4) x cos x cos 3 x dx = (pi-3)/(16)

    Text Solution

    |

  6. Prove that int(0)^(oo) e^(-2x)(sin 2x + cos 2 x) dx = (1)/(2)

    Text Solution

    |

  7. Show that int(0)^(pi//2) (cos x)/((1+sin x)(2+sin x)) dx = log((4)/(3...

    Text Solution

    |

  8. Show that int(1)^(7thsqrt(2))(1)/(x(2x^(7) + 1))dx=(1)/(7) log((6)/(5)...

    Text Solution

    |

  9. Show that int(0)^(pi//2)(sin x cos x)/(cos^(2) x + 3 cos x + 2)dx = lo...

    Text Solution

    |

  10. Show that int(0)^(1//3)(dx)/((1+x^(2))sqrt(1-x^(2))) = (pi)/(4sqrt(2))

    Text Solution

    |

  11. Show that int(0)^(1)(dx)/((1+x^(2))sqrt(2+x^(2))) = (pi)/(6)

    Text Solution

    |

  12. Show that int(0)^(1//2) (dx)/((1-2x^(2))sqrt(1-x^(2))) = (1)/(2) log(2...

    Text Solution

    |

  13. int(0)^(log5)(e^(x)sqrt(e^(x)-1))/(e^(x)+3)dx=

    Text Solution

    |

  14. Show that int(0)^(pi//2) (cos^(2) theta)/(cos^(2) theta + 4 sin^(2)...

    Text Solution

    |

  15. Show that int(0)^(pi//4) sqrt(tan theta) d theta = (1)/(sqrt(2)) log(s...

    Text Solution

    |

  16. Show that int(0)^(pi//4)(dx)/(cos^(4)x - cos^(2)x sin^(2) x + sin^(4)x...

    Text Solution

    |

  17. Show that int(0)^(pi//2)(sinxcos x)/(1+sin^(4)x)dx = (pi)/(8)

    Text Solution

    |

  18. Prove that int(0)^(pi//2)(cos^(2) x sin x)/(sqrt(1+cos^(2)x))dx = (sqr...

    Text Solution

    |

  19. Show that int(0)^(oo) (dx)/((x+sqrt(1+x^(2)))^(n))=(n)/(n^(2)-1), (n i...

    Text Solution

    |

  20. int(0)^(pi//4)[sqrt(tan x) + sqrt(cot x)] = dx

    Text Solution

    |