Originally Posted by

**BlueBeast** Hey brainys,

I was wondering how to derive a formula for a length of projectiles path in the air (2 dimensions). I figured out the relationship of x and y, y=x*tg(a) - gx^{2}/2v_{0}^{2}cos^{2}(a)

Then i combined some logic with the mean value theorem and got that lenght of path is integral from zero to x=v_{0}^{2}sin(2a)/g of sqrt(1 + (tg(a) - xg/v_{0}^{2}cos^{2}(a))^{2}) dx

When we raise (tg(a) - xg/v_{0}^{2}*cos^{2}(a))^{2 }and simplify a little bit we get **integral from zero to x=v**_{0}^{2}sin(2a)/g of sqrt((v_{0}^{4}cos^{2}(a) - 2v_{0}^{2}sin^{2}(a)*xg + x^{2}g)/v_{0}^{4}cos^{4}(a)) dx . Any ideas how to solve it? Thank you!