Evaluate the improper integral integral15 (1)/(sqrt(x-1))dx and determine whether it converges or diverges.

Here are the solutions to the remaining questions:

(a) (iii) Curve Rectification
Curve rectification is the process of determining the arc length of a curve. In calculus, it involves using integration to calculate the length of a curve segment between two specified points.

(b) Evaluate and determine whether the integral converges or diverges.

(i) $\int_{1}^{5} \frac{1}{\sqrt{x-1}}\,dx$
This is an improper integral because the integrand is undefined at $x=1$.

Step 1: Rewrite the integral as a limit.

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