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MMLU-Pro / 8296 / compute the integral iint_{Sigma} x^3 dy*dz +y^3 dz*dx+z^3 dx*dy, where is…

Problem

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

question

compute the integral $\iint_{\Sigma} x^3 dy*dz +y^3 dz*dx+z^3 dx*dy$, where is the outward of the ellipsoid x^2+y^2+z^2/4=1. Round the answer to the thousands decimal.
Plain-text mathematical notation (without MathML)
compute the integral $\iint_{\Sigma} x^3 dy*dz +y^3 dz*dx+z^3 dx*dy$, where is the outward of the ellipsoid x^2+y^2+z^2/4=1. Round the answer to the thousands decimal.
Original LaTeX notation
compute the integral $\iint_{\Sigma} x^3 dy*dz +y^3 dz*dx+z^3 dx*dy$, where is the outward of the ellipsoid x^2+y^2+z^2/4=1. Round the answer to the thousands decimal.

category

math

options

  1. 31.41592654
  2. 25.67890123
  3. 30.15928896
  4. 27.65432109
  5. 34.56789012
  6. 26.78901234
  7. 33.33333333
  8. 32.98765432
  9. 29.12345678
  10. 28.17283950

src

theoremQA-Math

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Source and history

upstream_id / Original problem ID
8296
task_id
954a6c99-f0da-537b-9b41-43d2c622738b
task_key
default--test--8296
task_revision_id
1
config / split
default / test

Official source

initial import