If [tex]f(\theta)[/tex] is given by:[tex]f(\theta) = 6cos^3(\theta)[/tex] and [tex]g(\theta)[/tex] is given by:[tex]g(\theta) = 6sin^3(\theta)[/tex](adsbygoogle = window.adsbygoogle || []).push({});

Find the total length of the astroid described by [tex]f(\theta)[/tex] and [tex]g(\theta)[/tex].

(The astroid is the curve swept out by ([tex]f(\theta)[/tex],[tex]g(\theta)[/tex]) as [tex]\theta[/tex] ranges from 0 to 2pi )

[tex]f/d(\theta) = -18*cos(x)^2*sin(x)[/tex]

[tex]g/d(\theta) = 18*sin(x)^2*cos(x)[/tex]

this is asking for arclength right?

my integral:

[tex]\int_{0}^{2\pi}\sqrt{(-18*cos(\theta)^2*sin(\theta))^2+(18*sin(\theta)^2*cos(\theta))^2}[/tex]

anyone what's wrong with my integral? cause i keep getting the wrong answer.

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# Homework Help: Another parametric question

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