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Math Help - Antiderivative

  1. #1
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    Post Antiderivative

    Which is the easiest method to find the antiderivative of (2t-3).

    I know that this may be an easy one, I just need to see ways of finding out how to find an antiderivative.
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  2. #2
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    Quote Originally Posted by katchat64 View Post
    Which is the easiest method to find the antiderivative of (2t-3).

    I know that this may be an easy one, I just need to see ways of finding out how to find an antiderivative.
    Integrate it with respect to t!

     \int 2t-3 dt = \frac{2t^2}{2} - 3t + C

     = t^2 - 3t + C
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  3. #3
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    Lightbulb

    Ok.... I already have to do that, so then it just makes the problem a lot easier right?
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  4. #4
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    Lightbulb

    Say I need to substitute 2 & 0, how would the problem look?
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    If you're a beginner, it helps to write every term (if possible) in the form

    ax^n.

    Then you can remember that the antiderivative is

    \frac{a}{n + 1}x^{n + 1} + C.


    So in this case, you'd have 2t^1 + 3t^0.

    Can you find this antiderivative using the formula?


    If you're finding a definite integral, once you have the antiderivative, substitute the upper limit and see what you have ( F(b), substitute the lower limit ( F(a)) and see what you have, then do F(b) - F(a).
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  6. #6
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    Lightbulb Evaluate the Integral

    \int_0^2{(2t-3)\,dx}

    What I got for the antiderivative of (2t-3) is (t^2-3t)

    I substituted 2 & 0 and the answer I got is (-2)

    Is this the right answer?
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  7. #7
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    Quote Originally Posted by katchat64 View Post
    \int_0^2{(2t-3)\,dx}

    What I got for the antiderivative of (2t-3) is (t^2-3t)

    I substituted 2 & 0 and the answer I got is (-2)

    Is this the right answer?
    Your antiderivative F(x) = t^2 - 3t.

    F(2) = 2^2 - 3(2) = 4 - 6 = -2.

    F(0) = 0^2 - 3(0) = 0

    F(2) - F(0) = -2 - 0 = -2.


    So yes it's correct
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  8. #8
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    Talking

    Thanks so much!
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