# Math Help - Find the length of the curve

1. ## Find the length of the curve

I have tried this one over and over and can't get the right answer. Can anyone help?

Consider the parametric equation
x = 16(cosθ+ θsinθ)
y = 16(sinθ− θcosθ)
What is the length of the curve for θ = 0 to θ = [3/10] π?

I have L=sqrt (dx/dt)^2 + (dy/dt)^2
dx/dt = 16t (sin(t)+sin(t)+t cos(t))
dy/dt= 16t (-cos(t)-cos(t)+t sin(t))

Is that right?

2. You will use the arclength formula
$L = \int_0^{\frac{3}{10}n} \! \sqrt{\left(\frac{dx}{d\theta}\right)^2 + \left(\frac{dy}{d\theta}\right)^2}\,dt$.
$\frac{dx}{d\theta} = 16\left(-\sin \theta + \sin \theta + \theta \cos \theta\right) = 16\cdot \theta \cos \theta$
$\frac{dy}{d\theta} = 16\left(\cos \theta - \cos \theta + \theta \sin \theta\right) = 16\cdot \theta \sin \theta$
Now substitute this into the arclength formula and remember $\cos^2 \theta + \sin^2 \theta = 1$.