Calculating Arc Length in Polar Coordinates

[JosephR]

Homework Statement

Find The length of r=sin³(x/3) 0<x<3pi/2

2. The attempt at a solution

well first i found r'=3.cos(x/3).1/3.sin²(x/3)=cos(x/3)sin²(x/3)
r²=cos²(x/3)sin^4(x/3)

then i put the formula

integral of radical (r'²+r²)dx and I'm stuck here

any help?

 

[tiny-tim]

Find The length of r=sin³(x/3) 0<x<3pi/2
…
well first i found r'=3.cos(x/3).1/3.sin²(x/3)=cos(x/3)sin²(x/3)
r²=cos²(x/3)sin^4(x/3)

then i put the formula

integral of radical (r'²+r²)dx and I'm stuck here

any help?

Hi JosephR!

Hint: sin⁶(x/3) = sin²(x/3)sin^4(x/3)

 

[JosephR]

hey tiny-tim:)

i knew this but it would take some time to be solved !

because sin²(x/3)=[1-cos(2x/3)]/2

anyway thanks buddy !