Length of the major axis of the ellipse 3x^2 + 2y^2 =6
Express in standard form by dividing by 6,
$\displaystyle \frac{x^2}{2}+\frac{y^2}{3}=1$
Thus,
$\displaystyle \frac{x^2}{(\sqrt{2})^2}+\frac{y^2}{(\sqrt{3})^2}= 1$
Thus, the semi y-axis is $\displaystyle \sqrt{3}$ and the semi x-axis is $\displaystyle \sqrt{2}$. Since, $\displaystyle \sqrt{3}>\sqrt{2}$ it is the one which contains the major axis. Thus, the total length of the major axis is $\displaystyle 2\sqrt{3}$