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MMLU-Pro / 8081 / Use divergence therem to evaluate iint_S vec{F} cdot d vec{S} where…

Problem

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

question

Use divergence therem to evaluate $\iint_S \vec{F} \cdot d \vec{S}$ where F→=xyi→−12y2j→+zk→\vec{F} = xy \vec{i} - \frac{1}{2}y^2\vec{j} + z\vec{k} and the surface SS consists of the three surfaces, $z=4 - 3*x^2 - 3y^2, 1 \le z \le 1$ on the sides and z=0z=0 on the bottom.
Plain-text mathematical notation (without MathML)
Use divergence therem to evaluate $\iint_S \vec{F} \cdot d \vec{S}$ where (F)→=xy(i)→−(1)/(2)y²(j)→+z(k)→ and the surface S consists of the three surfaces, $z=4 - 3*x^2 - 3y^2, 1 \le z \le 1$ on the sides and z=0 on the bottom.
Original LaTeX notation
Use divergence therem to evaluate $\iint_S \vec{F} \cdot d \vec{S}$ where $\vec{F} = xy \vec{i} - \frac{1}{2}y^2\vec{j} + z\vec{k}$ and the surface $S$ consists of the three surfaces, $z=4 - 3*x^2 - 3y^2, 1 \le z \le 1$ on the sides and $z=0$ on the bottom.

category

math

options

  1. 15.707
  2. 6.283
  3. 7.853
  4. 2.718
  5. 9.425
  6. 4.000
  7. 11.000
  8. 3.142
  9. 12.566
  10. 0

src

theoremQA-Math

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Source and history

upstream_id / Original problem ID
8081
task_id
e10cd392-3645-5002-83b9-a9eac3f5e8b4
task_key
default--test--8081
task_revision_id
1
config / split
default / test

Official source

initial import