[Edited below] see the third post for a more detailed attempt to solve it
Problem: A curve is given in polar coordinates by r = fi^2 between -pi <= fi =< pi
Determine the length of the curve.
I recall a formula my teacher has given us: L(x) = $(using given limits of integration) SQRT (h^2(fi)) + [h'(fi)]^2) d(fi)
= This would give me
$SQRT (fi^2)^2 + (2fi)^2 d(fi)
So far so good, right?
$SQRT (fi)^4 + 4fi^2 d(fi)
I think Variable substititution would be good here
U = (fi)^4 + 4fi^2 d(fi)
DU/D(fi) = 4(fi)^3 + 8fi
Hmm How can i complete this?
could someone help me in detail, thanks