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 $\displaystyle \theta$.
You're familiar with the formula $\displaystyle L = \int_{t=a}^{t=b} \sqrt{\left( \frac{dx}{dt} \right)^2 + \left( \frac{dy}{dt} \right)^2 } \, dt$, right?
Make the appropriate substitutions. The integrand becomes t and the integration is therefore trivial ......