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Math Help - definite integration homework question

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    definite integration homework question

    Do i use integration by substitution???
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    Re: definite integration homework question

    Quote Originally Posted by asilvester635 View Post
    Do i use integration by substitution???

    What is the derivative of \frac{(x^3+8)^3}{9}~?
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    Re: definite integration homework question

    Quote Originally Posted by asilvester635 View Post
    Do i use integration by substitution???
    Yes you can use a substitution. Rewrite it as \displaystyle \begin{align*} \frac{1}{3} \int_{-2}^{4}{3x^2 \left( x^3 + 8 \right)^2\, dx} \end{align*} then let \displaystyle \begin{align*} u = x^3 + 8 \implies du = 3x^2 \, dx \end{align*} and note that \displaystyle \begin{align*} u(-2) = 0 \end{align*} and \displaystyle \begin{align*} u(4) = 72 \end{align*} and the integral becomes \displaystyle \begin{align*} \frac{1}{3} \int_0^{72}{u^2\,du} \end{align*}.

    I'm sure you can go from here.
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    Re: definite integration homework question

    cool but why did you ad 1/3 at the front? is it because you added 3 by x^2?
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    Re: definite integration homework question

    Yes, the 3 inside the integrand has to be countered by the 1/3 in front so that the net effect is to multiply by 1.
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