definite integration homework question

• December 11th 2012, 11:36 AM
asilvester635
definite integration homework question
Do i use integration by substitution???
• December 11th 2012, 12:43 PM
Plato
Re: definite integration homework question
Quote:

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

What is the derivative of $\frac{(x^3+8)^3}{9}~?$
• December 11th 2012, 02:42 PM
Prove It
Re: definite integration homework question
Quote:

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.
• December 13th 2012, 09:05 PM
asilvester635
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?
• December 13th 2012, 09:18 PM
MarkFL
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.