# Curve lengths...

• Mar 29th 2008, 04:25 PM
N736RA
Curve lengths...
Not really sure how to approach this one:
Consider the parametric equation: x=5[cos(theta)+(theta)sin(theta)]
y=5[sin(theta)-(theta)cos(theta)]

What is the length of the curve for theta=0 to theta= (9/2)pi

Thanks
• Mar 29th 2008, 04:35 PM
mr fantastic
Quote:

Originally Posted by N736RA
Not really sure how to approach this one:
Consider the parametric equation: x=5[cos(theta)+(theta)sin(theta)]
y=5[sin(theta)-(theta)cos(theta)]

What is the length of the curve for theta=0 to theta= (9/2)pi

Thanks

Because I'm lazy, I'll use t instead of $\theta$.

You're familiar with the formula $L = \int_{t=a}^{t=b} \sqrt{\left( \frac{dx}{dt} \right)^2 + \left( \frac{dy}{dt} \right)^2 } \, dt$, right?

Make the appropriate substitutions. The integrand becomes t and the integration is therefore trivial ......
• Mar 29th 2008, 04:37 PM
N736RA
what was that formula? It showed up as "latex error: syntax error", thanks for the help! edit now i see it