Explain in detail how you use triple integrals to find the volume of the solid.

The solid generated by rotating the curve $r(t) = (t^2,t^3- t) $ with $t  \in [-1,1]$ around the y-axis.


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  • When you write "t=η (x(t))sign(t)", you mean "t=η (x(t))sin(t)" ?

  • M F H M F H

    No, sign(t) is the sign of t, -1 when t < 0 and +1 when t > 0. This is to get back the "full t" including its sign, when you take the square root of the square (which would otherwise always be positive).

  • M F H M F H

    Thanks for the coffee! 🙂

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