Calculate the volume of the solid bounded by the following surfaces: $y=x^2, y=1, x+y+z=4, z=0$.
How does on set up the integral?
2026-03-30 15:35:11.1774884911
Volume using double integrals
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$y=x^2$ is "parabola shifted infinitely" accordingly z-axis.
Your volume can be calculate by 2 and/or 3 dimensional integral:
$$\int_{-1}^{1}\int_{x^2}^{1}\int_{0}^{4-x-y}dxdydz= \int_{-1}^{1}\int_{x^2}^{1}(4-x-y)dxdy$$ Hope, you can finish it.