The function is and the interval is .

(a)

Graph :

Graph the function .

Observe the graph :

Green colour curve represents the function.

Pink colour represents the length of the curve over the interval .

(b)

Definition of Arc Length:

Let the function given by represent a smooth curve on the interval .

The arc length of between and is .

Consider .

Apply derivative on each side with respect to .

Derivative formula: .

.

Substitute and in .

.

(c)

The arc length is .

Consider the integrand as .

Graph the function on .

Observe the graph:

The value of the integral is .

Therefore, the arc length is about .

(a)

Graph of the function .

(b)  .

(c) Using integration capabilites of the graphing utility, the arc length is about .