# Thread: Arc Length Trig substitution

1. ## Arc Length Trig substitution

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

Here is what I have so far:

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

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

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

Now what?

2. I=integration(sec^3 A dA)=INT.[secA*sec^2AdA]

now,apply integration by parts,

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

3. Originally Posted by sbcd90

now,apply integration by parts,