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 ,t h e nt h ev a l u eof(4I-1)i s`

Text Solution

Verified by Experts

The correct Answer is:
0
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    MOTION|Exercise EXERCISE -4 LEVEL-I|15 Videos

  • CONTINUITY

    MOTION|Exercise EXERCISE - 4 (LEVEL -II) (PREVIOUS YEAR JEE ADVANCED)|5 Videos

  • DETERMINANTS

    MOTION|Exercise EXERCISE-4 (LEVEL-II)|6 Videos

Similar Questions

Explore conceptually related problems

Let f:R rarr R be a function defined by f(x)={[[x],x 2 where [x] is the greatest integer less than or equal to x. If I=int_(-1)^(2)(xf(x^(2)))/(2+f(x+1))dx, then the value of (4I-1) is

int_(0)^(15/2)[x-1]dx= where [x] denotes the greatest integer less than or equal to x

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

Let f(x)=[x^(2)+1],([x] is the greatest integer less than or equal to x) . Ther

Let f(x)=x[x], for every real number x , where [x] is the greatest integer less than or equal to x. Then,evaluate int_(-1)^(1)f(x)dx

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 f:Irarr I be defined by f(x)=[x+1] ,where [.] denotes the greatest integer function then f(x) is equal to

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

MOTION-DEFINITE INTEGRATION -EXERCISE -4 LEVEL-II
  1. T h ev a l u eofint(sqrt(1n2))^(sqrt(1n3))(xsinx^2)/(sinx^2+sin(1n6-x^...

    Text Solution

    |

  2. Let f:[1,oo] be a differentiable function such that f(1)=2. If int1...

    Text Solution

    |

  3. The value of the integral int(-pi//2)^(pi//2) (x^(2) + log" (pi-x)/(pi...

    Text Solution

    |

  4. Let f:[1/2,1]vecR (the set of all real numbers) be a positive, non-con...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  8. The integral overset(pi//2)underset(pi//4)int (2 cosecx)^(17)dx is equ...

    Text Solution

    |

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

    Text Solution

    |

  10. If alpha=int0^1(e^9x+3tan^((-1)x))((12+9x^2)/(1+x^2))dxw h e r etan^(-...

    Text Solution

    |

  11. Let f: RvecR be a continuous odd function, which vanishes exactly at o...

    Text Solution

    |

  12. Let f (x) = 7 tan ^(8) x + 7 tan ^(6) x - 3 tan ^(4) x - 3 tan ^(2) x ...

    Text Solution

    |

  13. Let f^(prime)(x)=(192 x^3)/(2+sin^4pix)fora l lx in Rw i t hf(1/2)=0....

    Text Solution

    |

  14. Let F : R to R be a thrice differentiable function . Suppose that F(...

    Text Solution

    |

  15. Let F : R to R be a thrice differentiable function . Suppose that F(...

    Text Solution

    |

  16. The total number of distincts x in [0,1] for which int(0)^(x) (t^(2))...

    Text Solution

    |

  17. Let f(x)=lim(n->oo)((n^n(x+n)(x+n/2)....(x+n/n))/(n!(x^2+n^2)(x^2+n^2/...

    Text Solution

    |

  18. Let f: R -> R be a differentiable function such that f(0)=0, f((pi/2))...

    Text Solution

    |

  19. For each positive integer n, let jy(n) =1/n ((n +1) (n +2) …(n +n) )...

    Text Solution

    |

  20. The value of the integral int0^(1/2)(1+sqrt(3))/(((x+1)^2(1-x)^6)^(...

    Text Solution

    |