# Triple Integration

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• Jul 4th 2010, 07:49 PM
sherryl
Triple Integration
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:

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

Is this on the right track?
• Jul 5th 2010, 05:03 AM
Ackbeet
Looks good so far. To avoid confusion, I would probably write the integral as

$\int_{0}^{\frac{1}{\sqrt {2} }} \int_{0}^{\sqrt {1-2x^{2}} } \int_{0}^{1-y} dz\,dy\,dx.$