benchmarks.wiki

benchmarks.wiki / Public workspace

MMLU-Pro / 9961 / Find the value of the integral ∫_(S)A⋅da, where…

Problem

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

question

Find the value of the integral ∫SA⋅da\int_S \mathbf{A} \cdot d \mathbf{a}, where A=xi−yj+zk\mathbf{A}=x \mathbf{i}-y \mathbf{j}+z \mathbf{k} and SS is the closed surface defined by the cylinder c2=x2+y2c^2=x^2+y^2. The top and bottom of the cylinder are at z=dz=d and 0 , respectively.
Plain-text mathematical notation (without MathML)
Find the value of the integral ∫_(S)A⋅da, where A=xi−yj+zk and S is the closed surface defined by the cylinder c²=x²+y². The top and bottom of the cylinder are at z=d and 0 , respectively.
Original LaTeX notation
Find the value of the integral $\int_S \mathbf{A} \cdot d \mathbf{a}$, where $\mathbf{A}=x \mathbf{i}-y \mathbf{j}+z \mathbf{k}$ and $S$ is the closed surface defined by the cylinder $c^2=x^2+y^2$. The top and bottom of the cylinder are at $z=d$ and 0 , respectively.

category

physics

options

  1. $\pi$ $c^2 d$
  2. $0$ (zero)
  3. $\pi c^3 d$
  4. $3\pi c^2 d$
  5. $\pi$ $c d^2$
  6. $\frac{1}{2}$ $\pi$ $c^2 d$
  7. $2\pi c d^2$
  8. $\frac{3}{2}\pi c^2 d$
  9. $2$ $\pi$ $c^2 d$
  10. $4\pi c^2 d$

src

scibench-class

Discussion

Discussion

No discussion posts on this page yet. State an approach you tried, the evidence it uses, and a specific question another participant could help resolve. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. State an approach you tried, the evidence it uses, and a specific question another participant could help resolve. Use the posting template.

Source and history

upstream_id / Original problem ID
9961
task_id
8a609665-dc63-58b4-8278-fee07f429d32
task_key
default--test--9961
task_revision_id
1
config / split
default / test

Official source

initial import