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MMLU-Pro / 8202 / Use Stoke's Theorem to evaluate iint_S curl vec{F} cdot d vec{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 $\iint_S curl \vec{F} \cdot d \vec{r}$ where F→=z2i→−3xyj→+x3y3k→\vec{F} = z^2 \vec{i} - 3xy \vec{j} + x^3y^3 \vec{k} and SS is the part of z=5−x2−y2z = 5 - x^2 - y^2 above the plane zz=1. Assume that S is oriented upwards.
Plain-text mathematical notation (without MathML)
Use Stoke's Theorem to evaluate $\iint_S curl \vec{F} \cdot d \vec{r}$ where (F)→=z²(i)→−3xy(j)→+x³y³(k)→ and S is the part of z=5−x²−y² above the plane z=1. Assume that S is oriented upwards.
Original LaTeX notation
Use Stoke's Theorem to evaluate $\iint_S curl \vec{F} \cdot d \vec{r}$ where $\vec{F} = z^2 \vec{i} - 3xy \vec{j} + x^3y^3 \vec{k}$ and $S$ is the part of $z = 5 - x^2 - y^2$ above the plane $z$=1. Assume that S is oriented upwards.

category

math

options

  1. -1.0
  2. 4.0
  3. -3.0
  4. 1.0
  5. 0.0
  6. 2.5
  7. 2.0
  8. -4.0
  9. 3.0
  10. -2.0

src

theoremQA-Math

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Source and history

upstream_id / Original problem ID
8202
task_id
bd6ce197-99b6-58d3-9894-c5f5b58c5008
task_key
default--test--8202
task_revision_id
1
config / split
default / test

Official source

initial import