Home
Class 12
MATHS
Let f be a non-negative function defined...

Let `f` be a non-negative function defined on the interval `[0,1]`. If `int_0^xsqrt(1-(f^(prime)(t))^2)dt=int_0^xf(t)dt ,0lt=xlt=1,a n d \ f(0)=0`, then

A

`f(1/2)lt 1/2` and `f(1/3)gt 1/3`

B

`f(1/2)gt 1/2` and `f(1/3)gt1/3`

C

`f(1/2)lt1/2` and `f(1/3)lt1/3`

D

`f(1/2)gt 1/2` and `f(1/3)lt 1/3`

Text Solution

Verified by Experts

The correct Answer is:
C
`f'=+-sqrt(1-f^(2))`
or `f(x)=sinx `or `f'(x)=-sinx` (not possible)
`:. f(x)=sinx`
Also `xgtsinxAAxgt0`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    CENGAGE ENGLISH|Exercise JEE MAIN|12 Videos

  • CURVE TRACING

    CENGAGE ENGLISH|Exercise EXERCISES|24 Videos

  • DETERMINANT

    CENGAGE ENGLISH|Exercise Multiple Correct Answer|5 Videos

Similar Questions

Explore conceptually related problems

Let f be a function defined on the interval [0,2pi] such that int_(0)^(x)(f^(')(t)-sin2t)dt=int_(x)^(0)f(t)tantdt and f(0)=1 . Then the maximum value of f(x) is…………………..

If f(x)=int_0^x tf(t)dt+2, then

If f(x)=int_0^x(sint)/t dt ,x >0, then

Let f be a differentiable function on R and satisfying the integral equation x int_(0)^(x)f(t)dt-int_(0)^(x)tf(x-t)dt=e^(x)-1 AA x in R . Then f(1) equals to ___

Let f be a real-valued function defined on interval (0,oo) ,by f(x)=lnx+int_0^xsqrt(1+sint).dt . Then which of the following statement(s) is (are) true? (A). f"(x) exists for all in (0,oo) . " " (B). f'(x) exists for all x in (0,oo) and f' is continuous on (0,oo) , but not differentiable on (0,oo) . " " (C). there exists alpha>1 such that |f'(x)|<|f(x)| for all x in (alpha,oo) . " " (D). there exists beta>1 such that |f(x)|+|f'(x)|<=beta for all x in (0,oo) .

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

If int_(0)^(x)f(t)dt=e^(x)-ae^(2x)int_(0)^(1)f(t)e^(-t)dt , then

If int_0^xf(t) dt=x+int_x^1 tf(t)dt, then the value of f(1)

Let f(x),xgeq0, be a non-negative continuous function, and let f(x)=int_0^xf(t)dt ,xgeq0, if for some c >0,f(x)lt=cF(x) for all xgeq0, then show that f(x)=0 for all xgeq0.

If f(x)=int_0^x{f(t)}^(- 1)dt and int_0^1{f(t)}^(- 1)=sqrt(2), then

CENGAGE ENGLISH-DEFINITE INTEGRATION -JEE ADVANCED
  1. Let f be a non-negative function defined on the interval [0,1]. If int...

    Text Solution

    |

  2. The value of int0^1(x^4(1-x)^4)/(1+x^2)\ dx is

    Text Solution

    |

  3. Let f be a real-valued function defined on the inverval (-1,1) such th...

    Text Solution

    |

  4. The valued of int(sqrt(In2))^(sqrt(In3)) (x sinx^(2))/(sinx^(2)+sin(In...

    Text Solution

    |

  5. Let f:[-1,2]->[0,oo) be a continuous function such that f(x)=f(1-x)for...

    Text Solution

    |

  6. Let f:[1/2,1]->R (the set of all real numbers) be a positive, non-cons...

    Text Solution

    |

  7. Let f:[0,2]vecR be a function which is continuous on [0,2] and is diff...

    Text Solution

    |

  8. int((pi)/4)^((pi)/2)(2cosecx)^17 dx

    Text Solution

    |

  9. Let f prime(x)=(192x^3)/(2+sin^4 pix) for all x in RR with f(1/2)=0. I...

    Text Solution

    |

  10. Evaluate: int(-pi//2)^(pi//2)(x^2cosx)/(1+e^x)dx

    Text Solution

    |

  11. If In=int(-pi)^(pi) \ (sinnx)/((1+pi^x) \ sinx) \ dx, n=0,1,2,...... t...

    Text Solution

    |

  12. about to only mathematics

    Text Solution

    |

  13. Let S be the area of the region enclosed by y=e^-(x^2),y=0,x=0,a n dx=...

    Text Solution

    |

  14. Find a for which lim(n->oo) (1^a+2^a+3^a+...+n^a)/((n+1)^(a-1)[(na+1)+...

    Text Solution

    |

  15. Let f:[a,b]to[1,oo) be a continuous function and let g:RtoR be defined...

    Text Solution

    |

  16. Let f:(0,oo) in R be given f(x)=overset(x)underset(1//x)int e^(t+(1)...

    Text Solution

    |

  17. The option(s) with the values of aa n dL that satisfy the following eq...

    Text Solution

    |

  18. Let f(x)=7tan^8x+7tan^6x-3tan^4x-3tan^2x for all x in (-pi/2,pi/2) . ...

    Text Solution

    |

  19. find the period of sin(x/2)-cos(x/3) is

    Text Solution

    |

  20. Let f: Rvec(0,1) be a continuous function. Then, which of the followin...

    Text Solution

    |