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

`e ^(-1)`

B

`0`

C

`2e ^(-1)`

D

`1+ 2e^(-1)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    MOTION|Exercise EXERCISE -2 (LEVEL-II)|11 Videos
  • DEFINITE INTEGRATION

    MOTION|Exercise EXERCISE -3|55 Videos
  • DEFINITE INTEGRATION

    MOTION|Exercise ELEMENTRAY EXERCISE|47 Videos
  • CONTINUITY

    MOTION|Exercise EXERCISE - 4 (LEVEL -II) (PREVIOUS YEAR JEE ADVANCED)|5 Videos
  • DETERMINANTS

    MOTION|Exercise EXERCISE-4 (LEVEL-II)|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=

MOTION-DEFINITE INTEGRATION -EXERCISE -2 (LEVEL-I)
  1. If I (1) = int (0) ^(1) 2 ^(x ^(2)) dx, I (2) = int (0) ^(1) 2 ^(x ^(3...

    Text Solution

    |

  2. If u (n) = int (0) ^(pi//2) x ^(n) sin x dx, n in N then the value of ...

    Text Solution

    |

  3. The vlaue of the integral underset(-1)overset(3 )int ("tan"^(1)(x)/(...

    Text Solution

    |

  4. In = int0^(pi/4) tan^n x dx , then the value of n(l(n-1) + I(n+1)) is

    Text Solution

    |

  5. The value of the integral l = int(0)^(1) x(1-x)^(n) dx is

    Text Solution

    |

  6. Let I (1) = int (0) ^(1) (e ^(x) dx )/( 1 + x) and I (2) = int (0) ^(1...

    Text Solution

    |

  7. If f(x) is a function satisfying f(1/x)+x^2f(x)=0 for all nonzero x , ...

    Text Solution

    |

  8. If underset(0)overset(100)intf(x) dx = a, then underset(r=1)overset(10...

    Text Solution

    |

  9. If f(x) and g(x) are continuous functions, then int(In lamda)^(In (1//...

    Text Solution

    |

  10. underset(2-ln3)overset(3+ln3)int(ln(4+x))/(ln(4+x)+ln(9-x))dx is equal...

    Text Solution

    |

  11. If [x] stands for the greatest integer function, the value of overset(...

    Text Solution

    |

  12. Find the value of the function f(x)=1+x+int1^x((lnt)^2+2lnt) dt where ...

    Text Solution

    |

  13. If f(x)=e^(g(x))a n dg(x)=int2^x(tdt)/(1+t^4) then f^(prime)(2) has th...

    Text Solution

    |

  14. If f(x) is differentiable and int0^(t^2)xf(x)dx=2/5t^5, then f(4/(25))...

    Text Solution

    |

  15. If y(x)=\ int(pi^2//16)^(x^2)(cos xdotcossqrt(theta))/(1+sin^2sqrt(the...

    Text Solution

    |

  16. lim( n to oo) (sin ""(pi)/(2n) . sin ""(2pi)/(2n). sin ""(3pi)/(2n)......

    Text Solution

    |

  17. The value of underset( n rarroo)(lim) underset(r=1)overset(r=4n)(sum)(...

    Text Solution

    |

  18. lim(n->oo) (1^p+2^p+3^p+...........+n^p)/n^(p+1)

    Text Solution

    |

  19. Evaluate : lim(n-> oo) (1^4+2^4+3^4+...+n^4)/n^5 - lim(n->oo) (1^3+2^3...

    Text Solution

    |

  20. underset(n to oo)lim underset(r=1)overset(n)sum(1)/(n)e^(r//n) is

    Text Solution

    |