Arc Length of y^2=4(x+4)^3 from x=0 to x=2

[v0id19]

Homework Statement

Find the arc length of the equation $$y^2=4(x+4)^3$$ from $$x=0$$ to $$x=2$$

Homework Equations

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

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?

 

[Dick]

Substitute u=9x+37?

 

[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.