Type "Example 2.21 a" to see the graph in app[br][u][color=#0000ff]https://www.geogebra.org/3d/w2qrqjac[/color][/u]
Find the volume of the solid bounded by planes z=1-x[sup]2[/sup] and y+x=1 in the first octant.[br][img]data:image/png;base64,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[/img]
[math]\frac{5}{12}[/math]unit[sup]3 [/sup]