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MMLU-Pro / 8185 / Use Stoke's Theorem to evaluate ∫_(C)(F)→⋅d(r)→ where …

Problem

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

question

Use Stoke's Theorem to evaluate ∫CF→⋅dr→\int_C \vec{F} \cdot d \vec{r} where F→=z2i→+y2j→+xk→\vec{F} = z^2 \vec{i} + y^2 \vec{j} + x \vec{k} and CC is the triangle with vertices (1,0,0), (0,1,0) and (0,0,1) with counter-clockwise rotation.
Plain-text mathematical notation (without MathML)
Use Stoke's Theorem to evaluate ∫_(C)(F)→⋅d(r)→ where (F)→=z²(i)→+y²(j)→+x(k)→ and C is the triangle with vertices (1,0,0), (0,1,0) and (0,0,1) with counter-clockwise rotation.
Original LaTeX notation
Use Stoke's Theorem to evaluate $\int_C \vec{F} \cdot d \vec{r}$ where $\vec{F} = z^2 \vec{i} + y^2 \vec{j} + x \vec{k}$ and $C$ is the triangle with vertices (1,0,0), (0,1,0) and (0,0,1) with counter-clockwise rotation.

category

math

options

  1. 0.166
  2. -1.000
  3. -0.166
  4. 0.333
  5. 0.500
  6. 0.666
  7. -0.333
  8. -0.500
  9. -0.666
  10. 1.000

src

theoremQA-Math

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Source and history

upstream_id / Original problem ID
8185
task_id
446d2687-adf1-52a6-b0f2-1ed0f53c43f4
task_key
default--test--8185
task_revision_id
1
config / split
default / test

Official source

initial import