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Let F(x) be the antiderivative of f(x)=3...

Let `F(x)` be the antiderivative of `f(x)=3 cosx-2sinx` whose graph passes through the point `((pi)/(2),1)`. Then `F((pi)/(3))` is equal to……..

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Knowledge Check

  • The anti - derivative of f(x) = e^(x//2) whose graph passes through the point (0,3) is :

    A
    `3e^(x//2)`
    B
    `4 e^(x//2-1)`
    C
    `2e^(x//2+1)`
    D
    None of these

  • The antiderivative of f (x) = log (log x ) + 1/(log x)^(2) whose graph passes through (e,e) is

    A
    `x (log (log x) + (log x)^(-1))`
    B
    `x (log (log x)- (log x)^(-1)) + e`
    C
    `x(log(logx)-(logx)^(-1)+2e`
    D
    none of these

  • If f(x)=|cosx| ,then f'(3pi)/(4) is equal to

    A
    `(1)/(sqrt2)`
    B
    `sqrt2`
    C
    `(1)/(2)`
    D
    `2sqrt2`