An Arc Length Investigation.

The article investigates the arc length of a smooth curve. Pythagorean theorem is the basis of the derivation of the formula for arc length, which is typically presented as a definite integral from x = a to x = b. The derivation of the formula is confined to measuring the portion of the graph that begins at x=0. The details of the derivation of the formula of arc length is presented. The explanation to the theory behind the concept of the special form of integrand is also discussed in detail. The author concluded that the investigation of the new function leads to greater understanding of the connection between integrals and area.