Home
Class 12
MATHS
Find the value of the function f(x)=1+x+...

Find the value of the function `f(x)=1+x+int_1^x((lnt)^2+2lnt) dt` where `f'(x)` vanishes

A

`1/e`

B

0

C

`2/e`

D

`1+2/e`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE AND DEFINITE INTEGRATION

    VK JAISWAL|Exercise EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)|16 Videos

  • INDEFINITE AND DEFINITE INTEGRATION

    VK JAISWAL|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|17 Videos

  • HYPERBOLA

    VK JAISWAL|Exercise Exercise-4 : Subjective Type Problems|3 Videos

  • INVERSE TRIGONOMETRIC FUNTIONS

    VK JAISWAL|Exercise Exercise-5 : Subjective Type Problems|6 Videos

Similar Questions

Explore conceptually related problems

Find the value of the function f(x)=1+x+int_(1)^(x)((ln t)^(2)+2ln t)dt where f'(x) vanishes

Find the range of the function f (x) = int _(0) ^(x) |t-1| dt, where 0 le x le 2

Find the deriative of the function f (x) = int _(0) ^(x) sqrt (1+ t ^(2)) dt.

Find the derivatives of the following functions : (a) F (x) = int_(1)^(x) " In t dt " (x gt 0) (b) F (x) = int_(2//x)^(x^(2)) (dt)/(t)

If f(x) = int_(x)^(x^(2)) t^(2)lnt then find f'(e)

f(x)=int_1^x lnt/(1+t) dt , f(e)+f(1/e)=

The range of the function f(x)=int_(1)^(x)|t|dt , x in[(-1)/(2),(1)/(2)] is

The least value of the function F(x) = int_(x)^(2) log_(1//3) t dt, x in [1//10,4] is at x=

VK JAISWAL-INDEFINITE AND DEFINITE INTEGRATION-EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. Find the value of the function f(x)=1+x+int1^x((lnt)^2+2lnt) dt where ...

    Text Solution

    |

  2. int (x+ ( cos^(-1)3x )^(2))/(sqrt(1-9x ^(2)))dx = (1)/(k (1)) ( sqrt(1...

    Text Solution

    |

  3. If int (0)^(oo) (x ^(3))/((a ^(2)+ x ^(2)))dx = (1)/(ka ^(6)), then fi...

    Text Solution

    |

  4. int( (x^2+1)dx)/x

    Text Solution

    |

  5. If int (x ^(6) +x ^(4)+x^(2)) sqrt(2x ^(4) +3x ^(2)+6) dx = ((ax ^(6) ...

    Text Solution

    |

  6. int( x^2+3)/(x^2+2)dx

    Text Solution

    |

  7. The value of int (tan x )/(tan ^(2) x + tan x+1)dx =x -(2)/(sqrtA) tan...

    Text Solution

    |

  8. Let int (0)^(1) (4x ^(3) (1+(x ^(4)) ^(2010)))/((1+x^(4))^(2012))dx = ...

    Text Solution

    |

  9. Let int ( 1) ^(sqrt5)(x ^(2x ^(2)+1) +ln "("x ^(2x ^(2x ^(2+1)))")")dx...

    Text Solution

    |

  10. If int (dx )/(cos ^(3) x-sin ^(3))=A tan ^(-1) (f (x)) +bln |(sqrt2+f ...

    Text Solution

    |

  11. Find the value of |a| for which the area of triangle included between ...

    Text Solution

    |

  12. Let I = int (0) ^(pi) x ^(6) (pi-x) ^(8)dx, then (pi ^(15))/((""^(15) ...

    Text Solution

    |

  13. int( x^3)/(x^2-3)dx

    Text Solution

    |

  14. If a continuous function f on [0,a] satisfies f(x)f(a-x)=1,agt0, then ...

    Text Solution

    |

  15. If {x} denotes the fractional part of x, then I = int (0) ^(100) (sqrt...

    Text Solution

    |

  16. int( x^3)/(x^2-2)dx

    Text Solution

    |

  17. IF M be the maximum valur of 72 int (0) ^(y) sqrt(x ^(4) +(y-y^(2))^(2...

    Text Solution

    |

  18. Find the number points where f (theta) = int (-1)^(1) (sin theta dx )/...

    Text Solution

    |

  19. underset(nrarroo)lim[(1)/(sqrtn)+(1)/(sqrt(2n))+(1)/(sqrt(3n))+...+(1)...

    Text Solution

    |

  20. The maximum value of int (-pi//2) ^(2pi//2) sin x. f (x) dx, subject t...

    Text Solution

    |

  21. Given a funtion g, continous everywhere such that g (1)=5 and int (0)^...

    Text Solution

    |