Home
Class 12
MATHS
If f(x)= underset(x)overset(x^2)int1/((l...

If `f(x)= underset(x)overset(x^2)int1/((log t)^2)dt ,x ne 1` then f(x)is monotomically

A

increasing on `(2,oo)`

B

incrasing on (1,2)

C

decreasing on `2(oo)`

D

decreasing on (0,3)

Text Solution

Verified by Experts

The correct Answer is:
A
We have
`f(x)=underset(x)overset(x^2)int(1)/((logt)^2)dt`
`rArr f(x)=2x(1)/((logx^2)^2)-1/((logx)^2)=((x-2)/(2))xx(1)/((log x)^2)`
Clearly `f(x) gt 0 " for all " x gt 2 `
Hence f(x) is increasing on `(2,oo)`
Promotional Banner

Topper's Solved these Questions

  • INCREASING AND DECREASING FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|8 Videos

  • INCREASING AND DECREASING FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|36 Videos

  • INCREASING AND DECREASING FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|18 Videos

  • HEIGHTS AND DISTANCES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|45 Videos

  • INDEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

Similar Questions

Explore conceptually related problems

If f(x)=overset(x)underset(0)int(sint)/(t)dt,xgt0, then

If y = underset(u(x))overset(v(x))intf(t) dt , let us define (dy)/(dx) in a different manner as (dy)/(dx) = v'(x) f^(2)(v(x)) - u'(x) f^(2)(u(x)) alnd the equation of the tangent at (a,b) as y -b = (dy/dx)_((a,b)) (x-a) If F(x) = underset(1)overset(x)inte^(t^(2)//2)(1-t^(2))dt , then d/(dx) F(x) at x = 1 is

If a function y=f(x) such that f'(x) is continuous function and satisfies (f(x))^(2)=k+underset(0)overset(x)int [{f(t)}^(2)+{f'(t)}^(2)]dt,k in R^(+) , then find f(x)

Let g(t) = underset(x_(1))overset(x_(2))intf(t,x) dx . Then g'(t) = underset(x_(1))overset(x_(2))int(del)/(delt) (f(t,x))dx , Consider f(x) = underset(0)overset(pi)int (ln(1+xcostheta))/(costheta) d theta . The number of critical point of f(x) , in the interior of its domain, is

If f(x)=int_(x^2)^(x^2+1)e^(-t^2)dt , then f(x) increases in

Let f(x) = int_(-2)^(x)|t + 1|dt , then

If f(x)=x^(2)int_(0)^(1)f(t)dt+2 , then

If f(x)=int_(1)^(x)(logt)(1+t+t^(2))dt AAxge1 , then prove that f(x)=f(1/x) .

Statement-1: If f(x)=int_(1)^(x) (log_(e )t)/(1+t+t^(2))dt , then f(x)=f((1)/(x)) for all x gr 0 . Statement-2:If f(x) =int_(1)^(x) (log_(e )t)/(1+t)dt , then f(x)+f((1)/(x))=((log_(e )x)^(2))/(2)

If overset(4)underset(-1)int f(x)=4 and overset(4)underset(2)int (3-f(x))dx=7 , then the value of overset(-1)underset(2)int f(x)dx , is

OBJECTIVE RD SHARMA ENGLISH-INCREASING AND DECREASING FUNCTIONS-Section I - Solved Mcqs
  1. Let f(x) and g(x) be defined and differntiable for all x ge x0 and f(x...

    Text Solution

    |

  2. If a lt 0 and f(x)=e^(ax )+ e^(-ax) is monotonically decreasing . F...

    Text Solution

    |

  3. If f(x)= underset(x)overset(x^2)int1/((log t)^2)dt ,x ne 1 then f(x)is...

    Text Solution

    |

  4. The interval in which the function f(x)=underset(0)overset(x)int((t...

    Text Solution

    |

  5. If f(x)=x^3+bx^2+cx+d and 0<b^2<c, then

    Text Solution

    |

  6. For the function f(x)=x cos ""1/x, x ge 1 which one of the following i...

    Text Solution

    |

  7. If the function g:(-oo,oo)rarr(-(pi)/(2),(pi)/(2)) is given by g(u)=...

    Text Solution

    |

  8. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

    Text Solution

    |

  9. Consider the polynomial f(x)=1 + 2x + 3x^2 +4x^3 for all x in R So...

    Text Solution

    |

  10. Consider the polynomial f(x) = 1+2x+3x^(2)+4x^(3) Let s be the sum...

    Text Solution

    |

  11. If f(x)=x^(3/2)(3x-10),xgeq0, then f(x) is increasing in .

    Text Solution

    |

  12. Let f(x) = log (sin x+ cos x), x in x (-pi/4,(3pi)/(4)) Then f is st...

    Text Solution

    |

  13. Let f(x) = (1-x)^(2) sin^(2)x+ x^(2) for all x in IR and let g(x) = un...

    Text Solution

    |

  14. f(x)=x|logex|,x gt 0 is monotonically decreasig in

    Text Solution

    |

  15. Let F:RtoR be a thrice differntiable function. Suppose that F(1)=0,F(3...

    Text Solution

    |

  16. Let f(x)=1-x-x^(3). Then, the real values of x satisfying the inequali...

    Text Solution

    |

  17. Let g(x)=f(sin x)+ f(cosx), then g(x) is decreasing on:

    Text Solution

    |

  18. Let f(x) be a monotonic polynomial of (2m-1) degree where m in N, then...

    Text Solution

    |

  19. Let f(x) =sin^4x+cos^4x. Then f is increasing function in the interval

    Text Solution

    |

  20. If f:R->R is a twice differentiable function such that f''(x) > 0 for ...

    Text Solution

    |