This problem is based on Example #1 in §12.1 of Stewart (pg 833).

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Estimate the volume of the solid that lies above the square $\displaystyle {R}={\left[{0},{2}\right]}\times{\left[{0},{2}\right]}$ and below the elliptic parabolid $\displaystyle {z}={15.8}-{x}^{{2}}-{2.1}{y}^{{2}}$. Divide $\displaystyle {R}$ into four equal squares and choose the sample point to be the upper right corner of each square $\displaystyle {R}_{{{i}{j}}}$. For your own benefit, you should consider sketching the solid and the approximating recatngular boxes.

Approximate volume = units³.