Physics I / Triple Integrals
Practice question · Estimate

0\int_{0}¹ 0\int_{0}¹ 01xyzdz\int_{0}^{1} xyz dz dy dx = ? Set the slider to your answer.

Estimate on a scale from 0 to 0.4.

Hints
  1. The integrand factors into three independent single-variable integrals.
  2. Each factor contributes one half; multiply them together.
Show the answer

0.125 (answers within ±0.004 count)

Why

= (01xdx\int_{0}^{1} x dx)(01ydy\int_{0}^{1} y dy)(01zdz\int_{0}^{1} z dz) = (12\frac{1}{2})(12\frac{1}{2})(12\frac{1}{2}) = 1/8 = 0.125.

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