Question

Sketch the space curve and find its length over the given interval.

Function                                                         Interval

Answer 1

Step 1:

The curve is and the interval is .

Arc length:

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

, where

Here , .

Consider .

Differentiate with respect to on each side.

Consider .

Differentiate with respect to on each side.

Consider .

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 .