Question: Define A(t) to be the arc length of the graph of y = f(x) from x = 0 to x = t, for t ≥ 0.
(a) Use the integral expression for arc length and a computer algebra system to obtain a formula for A(t).
(b) Graph A(t) for 0 ≤ t ≤ 10. What simple function does A(t) look like? What does this tell you about the approximate value of A(t) for large t?
(c) In order to estimate arc length visually, you need the same scales on both axes, so that the lengths are not distorted in one direction. Draw a graph of f(x) with viewing window 0 ≤ x ≤ 100, 0 ≤ y ≤ 100. Explain what you noticed in part (b) in terms of this graph.
f(x) = √x