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Math Help - Antiderivatives

  1. #1
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    Antiderivatives

    Find the general antiderivative of the function below.
    P(t) =

    Find the general antiderivative of the function below.

    F(t) =


    Find the general antiderivative of f(x) = 6x.

    F(x) =





    Find the general antiderivative of the function below.
    G(x) =




    Find an antiderivative F(x) with F '(x) = f(x) and F(0) = 0. f(x) = sin(x)
    F(x) =




    Evaluate the indefinite integral below.




    Evaluate the indefinite integral below.


    i need some help with these bad johnnys...any help would be killer...thanks

    mathlete
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by mathlete View Post
    Find the general antiderivative of the function below.
    P(t) =
    Hint: what is the derivative of sec(x)? what about tan(x)?



    Find the general antiderivative of the function below.

    F(t) =
    note that \frac {t^4 + 1}t = t^3 + \frac 1t

    for the first part, use the fact that F(t) = \int f(t)~dt

    now, \int x^n~dx = \frac {x^{n + 1}}{n + 1} + C .....this is known as the power rule for integrals

    for the second part, Hint: what is the derivative of ln(x)?


    Find the general antiderivative of f(x) = 6x.

    F(x) =
    use the power rule

    Find the general antiderivative of the function below.
    G(x) =
    use the power rule (Hint: you need to change the function a bit, to make it look like the form that the power rule applies to)

    Find an antiderivative F(x) with F '(x) = f(x) and F(0) = 0. f(x) = sin(x)
    F(x) =
    Hint: what is the derivative of -cos(x)?

    what is the anti-derivative of sin(x)? what if we plug in x = 0 into the anti-derivative?


    Evaluate the indefinite integral below.
    Hint: what is the derivative of arctan(x)?


    Evaluate the indefinite integral below.

    use the power rule
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