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

0 votes

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

asked Feb 18, 2015 in CALCULUS by anonymous
reshown Feb 18, 2015 by goushi

1 Answer

0 votes

Step 1:

The curve is .

Compare the curve with .

Here , .

Graph:

Grah the parametric equations  in the interval [0, 1].

Step 2:

Arc length:

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

, where

Differentiate with respect to on each side .

Differentiate with respect to on each side .

Substitute values in .

Step 3:

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

Let .

Differentiate with respect to on each side .

image

Change of integral limits:

Upper limit: If image, then image.

Lower limit: If image, then image.

Substitute  , image and limits of integral limits in the integral.

image

Solution:

Arc length of the curve is image.

answered Feb 23, 2015 by cameron Mentor
edited Feb 24, 2015 by cameron

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