Home
Class 12
MATHS
int1^elogx\ dx= 1 b. e-1 c. e+1 d. 0...

`int_1^elogx\ dx=` `1` b. `e-1` c. `e+1` d. `0`

Text Solution

Verified by Experts

`1 `
`int_{1}^{e} log x d x `
`=int_{1}^{e} log x x^{0} d x `
`=[x log x]_{1}^{e}-int_{1}^{e} frac{1}{x} x d x `
`=[x log x]_{1}^{e}-[x]_{1}^{e} `
`=(e-0)-(e-1) `
`=e-e+1 `
`=1`
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY

    RD SHARMA|Exercise Solved Examples And Exercises|277 Videos

  • DERIVATIVES AS A RATE MEASURER

    RD SHARMA|Exercise Solved Examples And Exercises|149 Videos

Similar Questions

Explore conceptually related problems

int_1^e (dx)/x

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

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

int_0^1 e^-x/(1+e^x)dx

The value of int_0^(pi//2)cosx\ e^(s in x)dx\ i s 1 b. e-1 c. 0 d. -1

[int_(1/e)^(e)|log x|dx=[ (A) e^(-1)-1, (B) 2(1-1/e), (C) 1-1/e, (D) None of thes ]]

int_(-1)^(1)e^(|x|)dx=2(e-1)

int_0^oo (xlogx)/(1+x^2)^2dx= (A) e (B) 1 (C) 0 (D) none of these

RD SHARMA-DEFINITE INTEGRALS-Solved Examples And Exercises
  1. 36/piint(pi//6)^(pi//3)(dx)/(1+sqrt(cotx)) equals to

    Text Solution

    |

  2. Given that int0^oo(x^2)/((x^2+a^2)(x^2+b^2)(x^2+c^2))dx=pi/(2(a+b)(b+c...

    Text Solution

    |

  3. int1^elogx\ dx= 1 b. e-1 c. e+1 d. 0

    Text Solution

    |

  4. int1^(sqrt(3))1/(1+x^2)dx is equal to pi/(12) b. pi/4 c. pi/6 d. pi/3

    Text Solution

    |

  5. The value of int0^(pi//2)cosx\ e^(sin x)dx\ i s 1 b. e-1 c. 0 d. -1

    Text Solution

    |

  6. If int0^a1/(1+4x^2)dx=\ pi/8 , then a equals pi/2 b. pi/4 c. 1/2 d. 1

    Text Solution

    |

  7. int0^1f(x)dx=1,\ int0^1xf(x)dx=a ,\ int0^1x^2f(x)dx=a^2,\ t h e n\ int...

    Text Solution

    |

  8. The value of int(-pi)^pisin^3xcos^2x\ dx\ is (pi^4)/2 b. (pi^4)/4 c. ...

    Text Solution

    |

  9. int(pi//6)^(pi//3)1/(sin2x)dx\ is equal to (log)e3 b. (log)"e"sqrt(3...

    Text Solution

    |

  10. int(-1)^1|1-x|dx is equal to -2 b. 2 c. 0 d. 4

    Text Solution

    |

  11. (lim)(n->oo){1/(2n+1)+1/(2n+2)++1/(2n+n)} I n\ (1/3) b. I n\ (2/3) c....

    Text Solution

    |

  12. The value of the integral int(-2)^2|1-x^2|dx is 4 b. 2 c. -2 d. 0

    Text Solution

    |

  13. int0^(pi//2)1/(1+cot^3x)dx is equal to 0 b. 1 c. pi//2 d. pi//4

    Text Solution

    |

  14. int0^(pi//2)(sinx)/(sin x+cos x)dx equals to pi//2 b. pi//4 c. pi//3 d...

    Text Solution

    |

  15. int0^(pi//2)xsinx\ dx is equal to pi//2 b. pi//4 c. pi d. 1

    Text Solution

    |

  16. int0^(pi//2)sin2xlogtanx\ dx\ is equal to pi//2 b. pi c. 0 d. 2pi

    Text Solution

    |

  17. The value of int0^pi1/(5+3cosx)dx is pi//2 b. pi//4 c. 0 d. pi//8

    Text Solution

    |

  18. int0^oolog(x+1/x)(dx)/(1+x^2)

    Text Solution

    |

  19. int0^(2a)f(x)dx is equal to 2int0^af(x)dx b. 0 c. int0^af(x)dx+int0^...

    Text Solution

    |

  20. If f(a+b-x)=f(x),\ t h e n\ inta^b xf(x)dx is equal to (a+b)/2inta^bf(...

    Text Solution

    |