Home
Class 12
MATHS
Let f: RvecR be a function defined by f...

Let `f: RvecR` be a function defined by `f(x)={[x],(xlt=2) \ \ (0,x >2)` where `[x]` is the greatest integer less than or equal to `xdot` If `I=int_(-1)^2(xf(x^2))/(2+f(x+1))dx , then \ the \ value \ of \ (4I-1)i s`

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

The function f(x)=(tan |pi[x-pi]|)/(1+[x]^(2)) , where [x] denotes the greatest integer less than or equal to x, is

Let [x] denotes the greatest integer less than or equal to x and f(x)=[tan^(2)x] . Then

The domain of the function f(x) = sqrt((4-x^(2))/([x]+2)) where [x] denotes the greatest integer less than or equal to x,is

The domain of the function f(x)=cos^(-1)[secx] , where [x] denotes the greatest integer less than or equal to x, is

If f(x)=|x|+[x] , where [x] is the greatest integer less than or equal to x, the value of f(-2.5)+f(1.5) is

Let f(x)=x-[x], for ever real number x ,w h e r e[x] is the greatest integer less than or equal to xdot Then, evaluate int_(-1)^1f(x)dx .

Let f(x) be defined by f(x) = x- [x], 0!=x in R , where [x] is the greatest integer less than or equal to x then the number of solutions of f(x) +f(1/x) =1

Let f(x) be defined by f(x) = x- [x], 0!=x in R , where [x] is the greatest integer less than or equal to x then the number of solutions of f(x) +f(1/x) =1

Let f(x)=max. {x+|x|,x-[x]} , where [x] denotes the greatest integer less than or equal to x, then int_(-2)^(2) f(x) is equal to

If the function f: R->R be such that f(x) = x-[x], where [x] denotes the greatest integer less than or equal to x, then f^-1(x) is

CENGAGE ENGLISH-INTEGRALS-All Questions
  1. If f(x)=cosx-int0^x(x-t)f(t)dt ,t h e nf^(primeprime)(x)+f(x) is equa...

    Text Solution

    |

  2. If f^(prime)(x)=f(x)+int0^1f(x)dx ,gi v e nf(0)=1, then the value of ...

    Text Solution

    |

  3. STATEMENT 1: int0^pisqrt(1-sin^2x) dx=0 , STATEMENT 2: int0^picosx dx...

    Text Solution

    |

  4. STATEMENT 1: Let m be any integer. Then the value of Im=int0^pi(sin2m ...

    Text Solution

    |

  5. STATEMENT 1: The value of int0^(2pi)cos^(99)x dx is 0 STATEMENT 2: in...

    Text Solution

    |

  6. For a epsilonR (the set of all real numbers) a!=-1, lim(n to oo) ((1^(...

    Text Solution

    |

  7. Let S be the area of the region enclosed by y-e^(-x^(2)),y=0, x=0 and ...

    Text Solution

    |

  8. Let f:(0,oo)vecR be given by f(x)=int(1/x)^x(e^(-(t+1/t))dt)/t , then ...

    Text Solution

    |

  9. Show that int0^pixf(sinx)dx=pi/2int0^pif(sinx)dxdot

    Text Solution

    |

  10. Let f(x) be a non-constant twice differentiable function defined on (-...

    Text Solution

    |

  11. Let f(x)=int2^x(dt)/(sqrt(1+t^4))a n dg(x) be the inverse of f(x) . Th...

    Text Solution

    |

  12. Let f be a real-valued function defined on interval (0,oo),by f(x)=lnx...

    Text Solution

    |

  13. Let f: R rarr R be a continuous odd function, which vanishes exactly a...

    Text Solution

    |

  14. If the value of the definite integral int0^1(sin^(-1)sqrt(x))/(x^2-x+1...

    Text Solution

    |

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

    Text Solution

    |

  16. The option(s) with the values of a and L that satisfy the following eq...

    Text Solution

    |

  17. Let f: RvecR be a function defined by f(x)={[x],(xlt=2) \ \ (0,x >2) ...

    Text Solution

    |

  18. Prove that int0^1tan^(-1)(1/(1-x+x^2))dx=2int0^1tan^(-1)x dx. Hence ...

    Text Solution

    |

  19. Let f(x)=|[secx,cosx,sec^2x+cotxcos ecx],[cos^2x,cos^2x, cosec^2x],[1,...

    Text Solution

    |

  20. If f(x)=inta^x[f(x)]^(-1)dx and inta^1[f(x)]^(-1)dx=sqrt(2), then

    Text Solution

    |