Stumped by Calculus question wording...?

Question

What does it mean to "find the exact length of the curve analytically?"

The question is:

A curve is given by x = 0~y Square Root (t^2 + 4t +3) dt for 3
Does it mean to just...graph it...? I really have no idea how to even begin this.

Please don't just give an answer -- I'm not even concerned with that. I just want a little hint on how to work this out b/c I'm completely stumped at this point.

Thank you in advance~

Answer 1

It means to use the definition of arc lenth (ie it's integral) and solve it.

recall that arc length = ∫sqrt(1+(dy/dx)^2) dx

an alternate definition using parametric representation is

∫sqrt((dx/dt)^2+(dy/dt)^2)dt

for x=x(t) and y=y(t)

Answer 2

Hint;
∫√(t^2 + 4t +3) dt
= ∫√[(t + 2)^2 - 1] dt

Answer 3

i think there's a site to help you