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find the volume of the spindle shaped solid obtained by revolving x^(2/3) + y^(2/3) =a^(2/3) about the x axis.


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volume of the spindle shaped solid obtained by revolving x^(2/3) + y^(2/3) =a^(2/3) about the x axis.
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change  over to parametric form with x = acos³θ ; y = asin³θ
dx = -3a cos² θ sinθ dθ 
use these in pi ∫ y²dx with suitable limits
answer and  some steps are given below
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hypocycloid


other  problems on applications of integration like area ,volume etc
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