# Thread: definite integration homework question

1. ## definite integration homework question

Do i use integration by substitution???

2. ## Re: definite integration homework question

Originally Posted by asilvester635
Do i use integration by substitution???

What is the derivative of $\frac{(x^3+8)^3}{9}~?$

3. ## Re: definite integration homework question

Originally Posted by asilvester635
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.

4. ## 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?

5. ## 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.