Home
Class 12
MATHS
If I=int(-1)^(1) {[x^(2)]+log((2+x)/(2-x...

If `I=int_(-1)^(1) {[x^(2)]+log((2+x)/(2-x))}dx` where [x] denotes the greatest integer less than or equal to x, the I equals

A

-2

B

-1

C

0

D

1

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA|Exercise Chapter Test 1|60 Videos

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA|Exercise Chapter Test 2|60 Videos

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA|Exercise Section II - Assertion Reason Type|12 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    OBJECTIVE RD SHARMA|Exercise Exercise|86 Videos

  • DERIVATIVE AS A RATE MEASURER

    OBJECTIVE RD SHARMA|Exercise Exercise|26 Videos

Similar Questions

Explore conceptually related problems

If I=int_(-1)^(1)([x^(2)]+log((2+x)/(2-x)))dx where denotes the greatest integer <=x, then I equals

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

If [x] denotes the greatest integer less than or equal to x, then ["log"_(10) 6730.4]=

lim_(xrarr oo) (log[x])/(x) , where [x] denotes the greatest integer less than or equal to x, is

Let [x] denote the greatest integer less than or equal to x. If x=(sqrt(3)+1)^(5), then [x] is equal to

Let f(x)=(x^(2)-9x+20)/(x-[x]) where [x] denotes greatest integer less than or equal to x), then

If f(x)=sin[pi^(2)]x+sin[-pi^(2)]x where [x] denotes the greatest integer less than or equal to x then

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

Consider the integral I=int_(0)^(10)([x]e^([x]))/(e^(x-1))dx , where [x] denotes the greatest integer less than or equal to x. Then the value of I is equal to :

OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Exercise
  1. The value of the integral int(0)^(pi//4) (sin theta+cos theta)/(9+16 s...

    Text Solution

    |

  2. Let (d)/(dx)(f(x))=(e^(sinx))/(x),x gt 0. "If" int1^(4) (3)/(x)e^(sinx...

    Text Solution

    |

  3. If I=int(-1)^(1) {[x^(2)]+log((2+x)/(2-x))}dx where [x] denotes the gr...

    Text Solution

    |

  4. The value of int(-pi//2)^(pi//2)(x^(2)+x cosx+tan^(5)x+1)dx is equal t...

    Text Solution

    |

  5. If int(-1)^(4) f(x)=4 and int(2)^(7) (3-f(x))dx=7, then the value of i...

    Text Solution

    |

  6. The value of I=int(0)^(pi//2) (1)/(1+cosx)dx is

    Text Solution

    |

  7. int(0)^(pi//2) (sin^(2)x)/(sinx+cosx)dxis equal to

    Text Solution

    |

  8. The value of the integral int(a)^(b) (|x|)/(x)dx, a lt b is

    Text Solution

    |

  9. The value of the integral int(0)^(2pi)(sin2 theta)/(a-b cos theta)d ...

    Text Solution

    |

  10. The value of the integral int(0)^(1) x(1-x)^(n)dx, is

    Text Solution

    |

  11. The value of the integral int(0)^(3alpha) cosec (x-alpha)cosec(x-2al...

    Text Solution

    |

  12. The value of the integral int(0)^(pi) (sin k x)/(sin x)dx (k is an eve...

    Text Solution

    |

  13. The value of the integral int(0)^(1)(1)/(x^(2)+2x cos alpha+1)dxis equ...

    Text Solution

    |

  14. The greater value of F(x)=int(1)^(x) |t|dt on the interval [-1//2,1//2...

    Text Solution

    |

  15. The value of the integral int(0)^(pi//2) |sin x-cos x|dx, is

    Text Solution

    |

  16. The value of the integral int(0)^(pi//4) sin^(-4)x dx, is

    Text Solution

    |

  17. The value of the integral I=int(1)^(oo) (x^(2)-2)/(x^(3)sqrt(x^(2)-1))...

    Text Solution

    |

  18. int(0)^(1) |sin 2pi x|dx id equal to

    Text Solution

    |

  19. The value of integral int(-pi)^(pi) (cos ax-sin b x)^(2)dx, where (a a...

    Text Solution

    |

  20. The value of the definite integral int(0)^(1)(1+e^(-x^(2))) dx is

    Text Solution

    |