Question

Find the length of the curve.

Answer 1

Step 1:

The curve is .

Arc length:

If the curve has the vector equation , then arc length of the curve is defined as,

, where.

Here , .

Differentiate with respect to on each side .

Differentiate with respect to on each side .

Differentiate with respect to on each side .

Step 2:

Substitute values in .

Substitute and limits of the integral in the arc length formula.

Solution:

Arc length of the curve is .