Question

Find the arc length of the graph of the function over the indicated interval.

Answer 1

Step 1:

The curve is , interval is .

Definition of the arc length:

If the curve , , then the length of the curve is defined as,

.

Here and .

Consider .

Differentiate with respect to on each side.

Step 2:

Substitute and limits of in arc length formula.

Solution:

The arc length of the curve is .

Answer 2

Step 1:

The curve is , interval is .

Definition of the arc length:

If the curve , , then the length of the curve is defined as,

.

Here and .

Consider .

Differentiate with respect to on each side.

Step 2:

Substitute and limits of in arc length formula.

Solution:

The arc length of the curve is .