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Let Lim(Trarroo) 1/T underset(0)overset(...

Let `Lim_(Trarroo) 1/T underset(0)overset(T)int(sinx+sinax)^(2)dx = L` then

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Knowledge Check

  • underset1overset2int 3x^2dx =???

    A
    9
    B
    7
    C
    `x^3+6`
    D
    3

  • Consider the function f : (-oo , oo) to (-oo , oo) defined by f(x) = (x^(2) - ax + 1)/(x^(2) + ax + 1) , 0 lt a lt 2 Let g (x) = underset(0) overset(e^(x))(int) (f'(t))/(1 + t^(2)) dt Which of the following is true ?

    A
    g'(x) is positive on `(-oo , 0)` and negative on `(0 , oo)`
    B
    g'(x) is negative on `(-oo, 0)` and positive on `(0,oo)`
    C
    g'(x) changes sign on both `(-oo , 0)` and `(0 , oo)`
    D
    g'(x) does not change sign on `(-oo , oo)`

  • lim_(trarr0) int_(0)^(2pi)(|sin(x+t)-sinx|)/(|t|)dx equals

    A
    2
    B
    4
    C
    43469
    D
    1

    • Similar Questions

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    Evaluate the following definite integrals underset(0)overset(pi//2)int(1+sinx)^(3)cosxdx

    Evaluate the following definite integrals underset(0)overset(1)int(dx)/(sqrt(1-x^(2)))

    Evaluate: (lim)_(x->0)(int underset0overset(x^2)cost^2tdt)/(xsinx)

    If overset(a)underset(0) int f(2a-x)dx = m and overset(a)underset(0)int f(x) dx=n , then overset(2a)underset(0) int f(x) dx is equal to

    Let L_(1) = lim_(xrarr0^(+)) (int_(0)^(x^(2)) sinsqrt(t)dt)/(x-sinx) , then identify the correct option(s).

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