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

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

Function                                                         Interval

asked Feb 18, 2015 in CALCULUS by anonymous

1 Answer

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Step 1:

The curve is image and the interval is image.

Arc length:

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

, where

Here image, image.

Consider image.

Differentiate with respect to on each side.

image

Consider image.

Differentiate with respect to on each side.

image

Consider image.

Differentiate with respect to on each side.

image

Step 2:

Substitute values in .

image

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

image

Solution:

Arc length of the curve image is image.

answered Feb 23, 2015 by cameron Mentor

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