Home
Class 12
MATHS
If |f(x)-f(y)|le2|x-y|^((3)/(2)) AAx,yin...

If `|f(x)-f(y)|le2|x-y|^((3)/(2))` `AAx,yinR` and `f(0)=1` then value of `int_(0)^(1)f^2(x)dx` is equal to (a) 1 (b) 2 (c) `sqrt2` (d) 4

A

`0`

B

`1/2`

C

`2`

D

`1`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    MCGROW HILL PUBLICATION|Exercise Questions from Previous Years. B-Architecture Entrance Examination Papers|18 Videos
  • DEFINITE INTEGRALS

    MCGROW HILL PUBLICATION|Exercise EXERCISE (LEVEL 2) Numerical Answer Type Questions|19 Videos
  • COMPLEX NUMBERS

    MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS. B-ARCHITECTURE ENTRANCE EXAMINATION PAPER|17 Videos
  • DETERMINANTS

    MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS B-ARCHITECTURE ENTRANCE EXAMINATION PAPERS|18 Videos

Similar Questions

Explore conceptually related problems

If |f(x)-f(y)|<=2|x-y|^((3)/(2))AA x,y in R and f(0)=1 then value of int_(0)^(1)f^(2)(x)dx is equal to (a) 1 (b) 2 (c) sqrt(2)(d)4

abs(f(x)-f(y))le(x-y)^2 forall x,y in R and f(0)=1 then

If 2f(x) - 3 f(1//x) = x," then " int_(1)^(2) f(x) dx is equal to

if int_(0)^(1)f(x)dx=1 and f(2x)=2f(x) then 3int_(1)^(2)f(x)dx is equal to

If f(x)=max{x^(2),(1-x)^(2),(3)/(4)},x in[0,1] then the value of of int_(0)^(1)f(x)dx is

Let f:R rarr R be a continuous function and f(x)=f(2x) is true AA x in R .If f(1)=3 then the value of int_(-1)^(1)f(f(x))dx is equal to (a)6(b) 0 (c) 3f(3)( d) 2f(0)

[ If f(x)=|x|+|x-1|, then int_(0)^(2)f(x)dx equals- [ (A) 3, (B) 2, (C) 0, (D) -1]]

If f(0)=1,f(2)=3,f'(2)=5 and f'(0) is finite,then int_(0)^(1)xf''(2x)dx is equal to (A) zero (B) 1(C)2(D) none of these

If f(x)=int(3x^(2)+1)/((x^(2)-1)^(3))dx and f(0)=0, then the value of (2)/(f(2))| is

f(0)=1 , f(2)=e^2 , f'(x)=f'(2-x) , then find the value of int_0^(2)f(x)dx

MCGROW HILL PUBLICATION-DEFINITE INTEGRALS-Questions from Previous Years. AIEEE/ JEE Main Papers
  1. If 2int0^1 tan^(-1)x dx= int0^1 cot^(-1)(1-x+x^2) dx then int0^1 tan^(...

    Text Solution

    |

  2. underset (n rarr infty )(lim) [((n+1)(n+2)...3n)/(n^(2n))]^(1//n) is e...

    Text Solution

    |

  3. int4^10([x^2])/([x^2-28 x+196]+[x^2])dx is (A) 3 (B) 5 (C) 7 (D) 9

    Text Solution

    |

  4. The integral int(pi/12)^(pi/4)(8cos2x)/((tanx+cotx)^3)dx equals

    Text Solution

    |

  5. If int(1)^(2) (dx)/( (x^(2) -2x + 4)^(3/2))=(k)/( k+5) then k is equal...

    Text Solution

    |

  6. int(pi//4)^(3pi//4)(dx)/(1+cos x)=

    Text Solution

    |

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

    Text Solution

    |

  8. If i is the greatest of the definite integrals I1=int0^1 e^-x cos ^2 ...

    Text Solution

    |

  9. The value of the integral int(-pi//2)^(pi//2) sin^(4) x (1+ log ((2+ s...

    Text Solution

    |

  10. The value of int(-pi//2)^(pi//2)(sin^(2)x)/(1+2^(x))dx is

    Text Solution

    |

  11. The value of int(0)^(pi)|cos x|^(3)dx is :

    Text Solution

    |

  12. If int(0)^(pi//3)(tantheta)/(sqrt(2ksectheta))d theta=1-(1)/(sqrt(2)),...

    Text Solution

    |

  13. lim(n rarr oo)((n)/(n^(2)+1^(2))+(n)/(n^(2)+2^(2)) + (n)/(n^(2)+3^(2))...

    Text Solution

    |

  14. If |f(x)-f(y)|le2|x-y|^((3)/(2)) AAx,yinR and f(0)=1 then value of int...

    Text Solution

    |

  15. The value of int(-pi//2)^(pi//2)(dx)/([x] + [ sin x] +4), where [t]...

    Text Solution

    |

  16. If int0^xf(t)dt=x^2+intx^1t^2f(t)dt, then f^(prime)(1/2) is

    Text Solution

    |

  17. The value of the integral underset(-2)overset2intsin^2x/(-2[x/pi]+1/2)...

    Text Solution

    |

  18. The integral int(1)^(e){((x)/(e))^(2x)-((e)/(x))^(x)} "log"(e)x dx is...

    Text Solution

    |

  19. Let f and g be continuous functions on [ 0 , a] such that f(x)=f(x)=...

    Text Solution

    |

  20. The integral int(pi//6)^(pi//4)(dx)/(sin2x(tan^(5)x+cot^(5)x)) equals

    Text Solution

    |