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Answers for “通过三重积分计算出的长方体的最终体积是多少?”

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The final volume of the rectangular box is 24 cubic units. This is obtained by evaluating the iterated triple integral ∫03∫04∫021 dz dy dx\int_{0}^{3}\int_{0}^{4}\int_{0}^{2} 1 \, dz \, dy \, dx from the inside out.

Conditions: The region is a rectangular box with bounds 0≤x≤30 \le x \le 3, 0≤y≤40 \le y \le 4, and 0≤z≤20 \le z \le 2.; The integrand is 1.

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The volume of the rectangular box is 24 cubic units. This is calculated by multiplying the side lengths 3, 4, and 2, or by evaluating the triple integral ∫03∫04∫021 dz dy dx\int_{0}^{3}\int_{0}^{4}\int_{0}^{2} 1 \, dz \, dy \, dx.

Conditions: The region is a rectangular box with bounds 0≤x≤30 \le x \le 3, 0≤y≤40 \le y \le 4, and 0≤z≤20 \le z \le 2.; The integrand is 1.