Question

<br />Find length of astroid,<br />x= a cos^3t and y=bsin^3t.​

Answer 1

Step-by-step explanation:

I want to find the arc length of the equation: x2/3+y2/3=4

My steps follow as:

y=f(x)=(4−x2/3)3/2

f′(x)=−x−1/3(4−x2/3)1/2

[f′(x)]2=4x−2/3−1

[f′(x)]2+1=4x−2/3

L=∫48√f′(x)2+1−−−−−−−−√dx=0.0955

Bounds of the upper integral are found by:

y=(4−x2/3)3/2=x

x=2 , x=8–√