Final answer:
To find the exact length of the curve y = sec(x) for 0 ≤ x ≤ π, we can use integration. The formula for finding the length of a curve given by y = f(x) from a to b is L = ∫ab √(1 + [f'(x)]2) dx. f'(x) = sec(x)tan(x).
Step-by-step explanation:
To find the exact length of the curve y = sec(x) for 0 ≤ x ≤ π, we can use integration. The formula for finding the length of a curve given by y = f(x) from a to b is L = ∫ab √(1 + [f'(x)]2) dx. In this case, f(x) = sec(x) and f'(x) = sec(x)tan(x). We can substitute these values into the formula and evaluate the integral to find the length of the curve.