Find volume of solid region in first octant by triple integration:

Solid is bounded by elliptic cylinder 2x²+y²=1 and the plane y+z=1

So far I've gotten to:

$\displaystyle \int\nolimits_{0}^{\frac{1}{\sqrt {2} }} {dx}\int\nolimits_{0}^{\sqrt {1-2x^{2}} } {dy}\int\nolimits_{0}^{1-y} {dz}$

Is this on the right track?