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MMLU-Pro / 8221 / Use Stokes' Theorem to evaluate ∫_(C)F⋅dr, where…

Problem

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

question

Use Stokes' Theorem to evaluate ∫CF⋅dr\int_C \mathbf{F} \cdot d \mathbf{r}, where F(x,y,z)=xyi+yzj+zxk\mathbf{F}(x, y, z)=x y \mathbf{i}+y z \mathbf{j}+z x \mathbf{k}, and CC is the triangle with vertices (1,0,0),(0,1,0)(1,0,0),(0,1,0), and (0,0,1)(0,0,1), oriented counterclockwise as viewed from above.
Plain-text mathematical notation (without MathML)
Use Stokes' Theorem to evaluate ∫_(C)F⋅dr, where F(x,y,z)=xyi+yzj+zxk, and C is the triangle with vertices (1,0,0),(0,1,0), and (0,0,1), oriented counterclockwise as viewed from above.
Original LaTeX notation
Use Stokes' Theorem to evaluate $\int_C \mathbf{F} \cdot d \mathbf{r}$, where $\mathbf{F}(x, y, z)=x y \mathbf{i}+y z \mathbf{j}+z x \mathbf{k}$, and $C$ is the triangle with vertices $(1,0,0),(0,1,0)$, and $(0,0,1)$, oriented counterclockwise as viewed from above.

category

math

options

  1. $-\frac{1}{2}$
  2. $\frac{1}{2}$
  3. $0$
  4. $\frac{3}{4}$
  5. $\frac{1}{4}$
  6. $-1$
  7. $\frac{1}{3}$
  8. $\frac{2}{3}$
  9. $-\frac{1}{4}$
  10. $-\frac{1}{3}$

src

scibench-calculus

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Source and history

upstream_id / Original problem ID
8221
task_id
16764b30-09b0-5f80-b721-c7995feeb075
task_key
default--test--8221
task_revision_id
1
config / split
default / test

Official source

initial import