Someone please help me with calc! how would i do this problem?

Question

set up, but do not evaluate, an integral that represents the
length of the curve
x=e^t +e^-t, y=5-2t, 0 less than or equal to t less than or equal to 3

Answer 1

L= Int (sqrt(dx^2+dy^2)
dx= (e^t-e^-t)dt
dy = -2dt
so L = Int(0,3) sqrt(e^2t+e-2t -2+4) dt = Int (0,3)( e^t+e^-t)dt =
e^t-e^-t (0,3)= e^3-1/e^3 -1+1 =e^3-1/e^3

Answer 2

S =

3
∫√(dx/dt)^2 + (dy/dt)^2)*dt
0

dx/dt= e^t -e^-t
(dx/dt)^2 = (e^t -e^-t)^2 = e^(2t) -2 +e^(-2t)

dy/dt=-2
(dy/dt)^2=4

S = ∫√((e^t -e^-t)^2+4)dt = ∫√(e^(2t) +2 +e^(-2t))dt

The above to be evaluated from t=0 to t=3