# Arc Length Integral Question

1. Feb 3, 2009

### v0id19

1. The problem statement, all variables and given/known data
Find the arc length of the equation $$y^2=4(x+4)^3$$ from $$x=0$$ to $$x=2$$

2. Relevant equations
$$L=\int_{a}^{b}\sqrt{1+f'(x)}dx$$

3. The attempt at a solution
$$L=\int_{0}^{2}\sqrt{1+9(x+4)}dx$$
which simplifies in to
$$L=\int_{0}^{2}\sqrt{9x+37}dx$$
and i'm stuck there--how should i try to integrate that?

2. Feb 3, 2009

### Dick

Substitute u=9x+37?

3. Feb 3, 2009

### v0id19

oh. wow. thanks.
now i feel kinda dumb lol i was making it more complicated than i had to, trying trig sub and stuff.
so $$dx=\frac{du}{9}$$.
sweet.