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Math Help - I think it is called an integral?

  1. #1
    Junior Member alane1994's Avatar
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    I think it is called an integral?

    Could someone check my math?

    \int(3x+2)^2 dx

    From that I got the answer.

    3x^3+6x^2+4x+C

    Is that correct? I used the sum rule, then I used the power rule to get this. Thanks for any feedback.
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  2. #2
    Behold, the power of SARDINES!
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    Re: I think it is called an integral?

    Quote Originally Posted by alane1994 View Post
    Could someone check my math?

    \int(3x+2)^2 dx

    From that I got the answer.

    3x^3+6x^2+4x+C

    Is that correct? I used the sum rule, then I used the power rule to get this. Thanks for any feedback.
    Yes that is correct. You can check your own answer by taking the derivative. Integrals (anti derivatives) and derivatives "undo" each other.
    Thanks from alane1994
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  3. #3
    Junior Member alane1994's Avatar
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    Re: I think it is called an integral?

    You take the derivative of 3x^3+6x^2+4x+C?
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    Re: I think it is called an integral?

    Quote Originally Posted by alane1994 View Post
    You take the derivative of 3x^3+6x^2+4x+C?
    Yes it gives

    9x^2+12x+4=(3x+2)^2 that was the integrand that you started with.
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    MHF Contributor MarkFL's Avatar
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    Re: I think it is called an integral?

    Another way to proceed is to let:

    u=3x+2\,\therefore\,du=3\,dx and we have:

    \frac{1}{3}\int u^2\,du=\frac{u^3}{9}+C=\frac{(3x+2)^3}{9}+C

    You can verify that this is equivalent to the form you gave.
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