find the length of the curve C from t=0 to t pi/2 where x(t)=2sin^3t and y(t)=2cos^3t. set up the correct integral and simplify the integrand.
i think im supposed to use the formula L= sqrt[(dx/dt)^2 + (dy/dt)^2]
for x' i got 36sin^4tcos^2t
y' = -36sin^2tcos^4t
how am i supposed to add(or subtract) them so that it =6sintcost ? that was the answer given for the part inside the integrand. so before rooting im supposed to get 36sin^2tcos^2t but how?
i think i might have screwed up on my math typing again...i wanted to say x=2sin^3(t) and y=2cos^3(t). just t not 3t so "sin and cos cubed t" o.o if not then i dont know how to get 3t...
whats the technique to deferentiate those trigs with cubes. can you go
or does the sign switch both times you differentiate? it becomes negative then postive again? or the sign only switches when you differentiate the last cos(t)?