Home
Class 12
MATHS
If int(cosx)^1(t^2f(t)dt=1-cosx AA x in ...

If `int_(cosx)^1(t^2f(t)dt=1-cosx AA x in (0,pi/2)`, then the value of `[f((sqrt(3))/4)]` is [.] denotes the greatest integer function) 4 (b) 5 (c) 6 (d) `-7`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES INVOLVING MEANS

    CENGAGE ENGLISH|Exercise Jee Advanced (Single|1 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE ENGLISH|Exercise MATRIX-MATCH TYPE|3 Videos

Similar Questions

Explore conceptually related problems

If [f((sqrt(3))/2)] is [.] denotes the greatest integer function) 4 (b) 5 (c) 6 (d) -7

The value of lim_(xto0)|x|^([cosx]) , [.] denotes greatest integer function is

The value of int_(0)^(x)[t+1]^(3) dt (where, [.] denotes the greatest integer function of x) is qeual to

Evaluate ("lim")_(x->(5pi)/4) [sinx+cosx], where [.] denotes the greatest integer function.

The range of the function f(x) =[sinx+cosx] (where [x] denotes the greatest integer function) is f(x) in :

Range of f(x) =[1+sinx]+[cosx-1]+[tan^(- 1)x] AA x in [0,2pi] where [] denotes the greatest integer function is

lim_(x-(pi)/(2)) [([sinx]-[cosx]+1)/(3)]= (where [.] denotes the greatest integer integer function)

f(x) = 1 + [cosx]x in 0 leq x leq pi/2 (where [.] denotes greatest integer function) then

The range of f(x)=[|sin x|+|cosx"|""]"dot Where [.] denotes the greatest integer function, is {0} (b) {0,1} (c) {1} (d) none of these

The sum of roots of the equation cos^(-1)(cosx)=[x],[dot] denotes the greatest integer function, is (a) 2pi+3 (b) pi+3 (c) pi-3 (d) 2 pi-3

CENGAGE ENGLISH-INTEGRALS-All Questions
  1. lim(x->0)1/x[inty^a e^(sin^2t)dt-int(x+y)^a e^(sin^2t)dt] is equal to

    Text Solution

    |

  2. A function f is continuous for all x (and not everywhere zero) such th...

    Text Solution

    |

  3. If int(cosx)^1(t^2f(t)dt=1-cosx AA x in (0,pi/2), then the value of [...

    Text Solution

    |

  4. If int0^ycost^2dt=int0^(x^2)(sint)/t dx ,t h ep rov et h a t(dy)/(dx)=...

    Text Solution

    |

  5. If int0^xf(t) dt=x+intx^1 tf(t)dt, then the value of f(1)

    Text Solution

    |

  6. Evaluate: lim(x->oo)((int0^xe^(x^2)dx)^2)/(int0^x e^(2x^2)dx)

    Text Solution

    |

  7. If f(x)=1+1/x int1^x f(t) dt, then the value of f(e^-1) is

    Text Solution

    |

  8. If int0^1e^ (-x^2) dx=a , then find the value of int0^1x^2e^ (-x^2) dx...

    Text Solution

    |

  9. Ifint0^(f(x))t^2dt=xcospix ,t h e nf^(prime)(9)i s -1/9 (b) -1/3 (c...

    Text Solution

    |

  10. IfIn=int0^pix^nsinx dx ,t h e n fin d t h e v a l u eof I5+20 I3dot

    Text Solution

    |

  11. The value of int0^1lim(n->oo)sum(k =0)^n(x^(k+2)2^k)/(k!)dx is: (a) e ...

    Text Solution

    |

  12. If I(n)=int(0)^(pi/2) sin^(n)x dx, then show that I(n)=((n-1)n)I(n-2)....

    Text Solution

    |

  13. If A=int0^1 x^(50)(2-2x)^(50)dx ,B=int0^1 x^(50)(1-x)^(50)dx , which ...

    Text Solution

    |

  14. If In=int0^1(dx)/((1+x^2)^n); n in N , then prove that 2nI(n+1)=2^(-n...

    Text Solution

    |

  15. Given that f satisfies |f(u)-f(v)|lt=|u-v| for u and v in [a , b]dot T...

    Text Solution

    |

  16. IfIn=int0^1x^n(tan^(-1)x)dx ,t h e np rov et h a t (n+1)In+(n-1)I(n-2...

    Text Solution

    |

  17. IfI=int(-20pi)^(20pi)|sinx|[sinx]dx(w h e r e[dot] denotes the greate...

    Text Solution

    |

  18. If Im=int1^x(logx)^mdx satisfies the relation (Im)=k-l I(m-1) then

    Text Solution

    |

  19. The value of the integral int0^1sqrt((1-x)/(1+x))dx i s (a)pi/2+1 (b...

    Text Solution

    |

  20. IfI(m , n)=int0^(pi/2)sin^m xcos^n xdx , Then show that I(m , n)=(m-1...

    Text Solution

    |