A particle moves in the xyxyxy-plane with x(t)=∫0tcos(u2)dux(t) = \int_0^t \cos(u^2) dux(t)=∫0tcos(u2)du and y(t)=∫0tsin(u2)duy(t) = \int_0^t \sin(u^2) duy(t)=∫0tsin(u2)du. Find the speed v(t)=(x′)2+(y′)2v(t) = \sqrt{(x')^2 + (y')^2}v(t)=(x′)2+(y′)2.
111
ttt
t2t^2t2
cos(t2)+sin(t2)\sqrt{\cos(t^2) + \sin(t^2)}cos(t2)+sin(t2)