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Find the arc length of the curve on the interval [0, 2π].

0 votes

Find the arc length of the curve on the interval [0, 2π].

Hypocycloid perimeter:  x = a cos3 θ, y = a sin3 θ

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

1 Answer

0 votes

Step 1:

Hypo cycloid perimeter: image, image.

Arc length of the curve:

If a curve image is described by parametric equations image and image,

where image are continuous on image, then the arc length of the curve image is

image.

Consider image.

Find  image.

image

Find image.

image

Step 2:

Substitute image and image values in the arc length formula.

image

Periodicity of image is .

In the interval , we can write integral as four multiples of single integral considering in .

Step 3:

image

image

Solution:

Arc length of the curve image is image.

answered Feb 19, 2015 by cameron Mentor

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