Home
Class 12
MATHS
Let In=int(-n)^n({x+1}*{x^2+2}+{x^2+3}{x...

Let `I_n=int_(-n)^n({x+1}*{x^2+2}+{x^2+3}{x^2+4})dx`, where { } denote the fractional part of x. Find `I_1.`

A

`-(1)/(3)`

B

`-(2)/(3)`

C

`(1)/(3)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Definite intefral Exercise 1 : Single Option Correct Type Questions|1 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|10 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise For Session 6|10 Videos

  • COORDINATE SYSTEM AND COORDINATES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

  • DETERMINANTS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos

Similar Questions

Explore conceptually related problems

Evaluate int_(0)^(2){x} d x , where {x} denotes the fractional part of x.

f(x)=sqrt((x-1)/(x-2{x})) , where {*} denotes the fractional part.

The value of int_(0)^(4) {x} dx (where , {.} denotes fractional part of x) is equal to

The range of the function y=sqrt(2{x}-{x}^2-3/4) (where, denotes the fractional part) is

The value of int_(1)^(4){x}^([x]) dx (where , [.] and {.} denotes the greatest integer and fractional part of x) is equal to

If f(n)=(int_0^n[x]dx)/(int_0^n{x}dx) (where,[*] and {*} denotes greatest integer and fractional part of x and n in N). Then, the value of f(4) is...

The value of x satisfying int_(0)^(2[x+14]){(x)/(2)} dx=int_(0)^({x})[x+14] dx is equal to (where, [.] and {.} denotes the greates integer and fractional part of x)

The value of int_(-5)^(5)f(x)dx, where f(x)="minimum"({x+1},{x-1}), ∀ x in R and {.} denotes fractional part of x, is equal to

int_(-1)^(2)[([x])/(1+x^(2))]dx , where [.] denotes the greatest integer function, is equal to

Consider the binomial expansion of R = (1 + 2x )^(n) = I + f , where I is the integral part of R and f is the fractional part of R , n in N . Also , the sum of coefficient of R is 2187. The value of (n+ Rf ) "for x" = (1)/(sqrt(2)) is

ARIHANT MATHS-DEFINITE INTEGRAL-Exercise (Single Option Correct Type Questions)
  1. For f(x) =x^(4) +|x|, let I(1)= int (0)^(pi)f(cos x) dx and I(2)= int(...

    Text Solution

    |

  2. Let f be a positive function. Let I(1)=int(1-k)^(k)x f[x(1-x)]dx , I(...

    Text Solution

    |

  3. Suppose that the quadratic function f(x) = ax^(2) + bx +c is non-negat...

    Text Solution

    |

  4. Let I (a) =int(0)^(pi) ((x)/(a)+ a sin x)^(2) dx where a is positive r...

    Text Solution

    |

  5. The set of value of 'a' which satisfy the equation int0^2(t-log2a)dt...

    Text Solution

    |

  6. lim(x rarr infty) (x^(3) int(-1//x)^(1//x)("In" (1+t^(2)))/(1+e^(t)) d...

    Text Solution

    |

  7. The value of sqrt(pi(int(0)^(2008)x| sinpi x| dx)) is equal to

    Text Solution

    |

  8. lim(n rarr infty) sum(k=1)^(n) (k)/(n^(2)+k^(2)),x gt 0 is equal to

    Text Solution

    |

  9. Let a gt 0 and f(x) is monotonic increase such that f(0)=0 and f(a)=b...

    Text Solution

    |

  10. Evaluate the definite integral: int0^1((xdx)/(1+x))

    Text Solution

    |

  11. The value of int (0)^(infty)e^-(a^(2)x) dx is equal to

    Text Solution

    |

  12. lim(lamda to 0)(int(0)^(1) (1+x)^(lambda ) dx)^(1//lambda) Is equal t...

    Text Solution

    |

  13. If 2f (x) +f (-x)=(1)/(x) sin (x-(1)/(x)), then the value of int(1//e...

    Text Solution

    |

  14. The value of the definite integral int(0)^(pi//2)sin x sin 2x sin 3x d...

    Text Solution

    |

  15. If f(x) is differentiable function and (f(x).g(x)) is differentiable a...

    Text Solution

    |

  16. The number of integral solutions of the equation 4int (0)^( infty)(log...

    Text Solution

    |

  17. int(0)^(16n^(2)//pi) "cos" (pi)/(2)[(xpi)/(n)] dx is equal to

    Text Solution

    |

  18. If int-2^-1 (ax^2-5)dx=0 and 5 + int1^2 (bx + c) dx = 0, then

    Text Solution

    |

  19. The value of int(3)^(6)(sqrt(x+sqrt(12x-36))+sqrt(x-sqrt(12x- 36)))dx...

    Text Solution

    |

  20. Let In=int(-n)^n({x+1}*{x^2+2}+{x^2+3}{x^2+4})dx, where { } denote the...

    Text Solution

    |