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MMLU-Pro / 8605 / compute the integral iint_V frac{d x d y d z}{(1+x+y+z)^3}, where V=(x, y,…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

compute the integral $\iint_V \frac{d x d y d z}{(1+x+y+z)^3}$, where V={(x, y, z): x, y, z \geq 0, x+y+z\leq 1}.
Plain-text mathematical notation (without MathML)
compute the integral $\iint_V \frac{d x d y d z}{(1+x+y+z)^3}$, where V={(x, y, z): x, y, z \geq 0, x+y+z\leq 1}.
Original LaTeX notation
compute the integral $\iint_V \frac{d x d y d z}{(1+x+y+z)^3}$, where V={(x, y, z): x, y, z \geq 0, x+y+z\leq 1}.

category

math

options

  1. 0.092
  2. 0.042
  3. 0.050
  4. 0.025
  5. 0.018
  6. 0.056
  7. 0.028
  8. 0.075
  9. 0.065
  10. 0.034

src

theoremQA-Math

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Source and history

upstream_id / Original problem ID
8605
task_id
d751c357-ca34-5be9-b3dd-e1f3c2671051
task_key
default--test--8605
task_revision_id
1
config / split
default / test

Official source

initial import