# Thread: Arc Length Trig substitution

1. ## Arc Length Trig substitution

Find the arc length:
$
y = \frac{1}{2} x^2$
from point P to point Q: $P(-3,\frac{9}{2})$ $Q(3,-\frac{9}{2})$

Here is what I have so far:

Length = $2 \int\limits^{3}_{0} \sqrt{1 + x^2} dx$

$= 2 \int\limits^{\sqrt{10}}_{1} \sqrt{tan^2\theta + 1} \cdot sec^2\theta d\theta$

$
= 2 \int\limits^{\sqrt{10}}_{1} sec^3\theta d\theta$

Now what?

now,apply integration by parts,

so,2I=secA*tanA+log(secA+tanA)

3. Originally Posted by sbcd90

now,apply integration by parts,