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Find the value of int(-1)^(1)[x^(2)+{x}]...

Find the value of `int_(-1)^(1)[x^(2)+{x}]dx`, where [.] and `{.}` denote the greatest function and fractional parts of `x`, respectiely.

Answer

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Knowledge Check

  • Number of solution of equation [x]^2=x+2{x} is/are , where [.] and {.} denote the greatest integer and the fractional part functions, respectively

    A
    4
    B
    3
    C
    2
    D
    1

  • The value of int_(-2)^2 (sin^2x)/([x/pi]+1/2) dx where [x] denotes the greatest integer lex is

    A
    1
    B
    0
    C
    4-sin 4
    D
    none of these

  • The value of int_1^2[2x^2-3] dx where [] denotes GIF is

    A
    4
    B
    `sqrt(-3/2)+sqrt2+sqrt3-10`
    C
    `9-(sqrt(3/2)+sqrt2+sqrt(5/2)+sqrt3+sqrt(7/2)`
    D
    `15-sqrt(3/2)-sqrt2-sqrt(5/2)-sqrt3-sqrt(7/2)-sqrt(9/2)`

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    If int_(0)^(x) [x] dx = int_(0)^([x]) xdx, x notin integer (where, [.] and {.} denotes the greatest integer and fractional parts respectively, then the value of 4{x} is equal to …

    Evaluate: int_(-pi/2)^(2pi)[cot^(-1)x]dx , where [dot] denotes the greatest integer function

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    If f(x)=(tanx)/(x) , then find lim_(xto0)([f(x)]+x^(2))^((1)/({f(x)})) , where [.] and {.} denotes greatest integer and fractional part function respectively.

    Evaluate: int_(-5)^5x^2[x+1/2]dx(w h e r e[dot] denotes the greatest integer function).

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