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MMLU-Pro / 7982 / 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→=sin(πx)i→+(zy3)j→+(z2+4x)k→\vec{F} = sin(\pi x) \vec{i} + (z y^3)\vec{j} + (z^2 + 4x)\vec{k} and SS is the suface of the box with −1≤x≤2,0≤y≤1-1 \le x \le 2, 0 \le y \le 1 and 1≤z≤41 \le z \le 4. Note that all six sides of the box are included in SS.
Plain-text mathematical notation (without MathML)
Use divergence therem to evaluate $\iint_S \vec{F} \cdot d \vec{S}$ where (F)→=sin(πx)(i)→+(zy³)(j)→+(z²+4x)(k)→ and S is the suface of the box with −1≤x≤2,0≤y≤1 and 1≤z≤4. Note that all six sides of the box are included in S.
Original LaTeX notation
Use divergence therem to evaluate $\iint_S \vec{F} \cdot d \vec{S}$ where $\vec{F} = sin(\pi x) \vec{i} + (z y^3)\vec{j} + (z^2 + 4x)\vec{k}$ and $S$ is the suface of the box with $-1 \le x \le 2, 0 \le y \le 1$ and $1 \le z \le 4$. Note that all six sides of the box are included in $S$.

category

math

options

  1. 80.1
  2. 69.0
  3. 60.5
  4. 72.3
  5. 91.4
  6. 83.7
  7. 58.6
  8. 75.2
  9. 67.5
  10. 54.8

src

theoremQA-Math

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Source and history

upstream_id / Original problem ID
7982
task_id
6ef3f497-9af8-50d9-a949-37412a020412
task_key
default--test--7982
task_revision_id
1
config / split
default / test

Official source

initial import