how are you? :) So, I'm having some trouble trying to calculate the volume of this (rotating around the x-axis)

$y ≥ 0 $ , $2x^2 + y^2 ≤ 1$

I know the second equation refers to an ellipse.

Thank you so much, and sorry for my poor English, it's my second language and it's very hard talking about math :s hahaha have a nice day :)


If you "solve" $2x^2+y^2=1$ you obtain in the upper half plane (because $y\geq 0$) the equation of the curve, that is, you get $y=f(x)=(1-2x^2)^{1/2}$. The formula for volume of a solid obtained when rotating the area bounded by the curve and $x$-axis about an $x$-axis is $V_f=\pi\displaystyle\int_a^b (f(x))^2dx$. So we only need to find the values of $a$ and $b$ and they are obtained when solving the equation $y=f(x)=0$. So solve and integrate now!


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