You will want to use the formula
Where v(t) is the speed function.
(2cost - cos2t, 2sint - sin2t) 0 <= t <= pi/2
Here's what I have so far:
x'(t)^2 = 4sin^2(t) - 8(sint)(sin2t) + 4sin^2(2t)
y'(t)^2 = 4cos^2(t) - 8(cost)(cos2t) + 4cos^2(2t)
x'(t)^2 + y'(t)^2 = 4 - 8(sint)(sin2t) + 4sin^2(2t) - 8(cost)(cos2t) +
4cos^2(2t)
What do I do next? And/or am I even doing it right?
Well, I'm wondering how I can integrate it as the resultant integrand will be:
integral( SQRT(4 - 8(sint)(sin2t) + 4sin^2(2t) - 8(cost)(cos2t) + 4cos^2(2t)), t, 0, pi/2 )
I'm not sure how I can simplify it when this part is in the square root: 8(sint)(sin2t) + 4sin^2(2t) - 8(cost)(cos2t) + 4cos^2(2t)
Thanks! By the way, shouldn't the integral you wrote at the end have a 4 in front of it?
I think the main part was that I didn't think that I was supposed to use things like angle sum/double angle/half angle (which, unfortunately, my teacher pre-calculus never taught) formulas.
Also, I was wondering, how did you get the text to look "nice"? Is there some sort of web app that does it for you?