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MMLU-Pro / 9139 / Find the value of the integral …

Problem

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

question

Find the value of the integral ∫S(∇×A)⋅da\int_S(\nabla \times \mathbf{A}) \cdot d \mathbf{a} if the vector A=yi+zj+xk\mathbf{A}=y \mathbf{i}+z \mathbf{j}+x \mathbf{k} and SS is the surface defined by the paraboloid z=1−x2−y2z=1-x^2-y^2, where z≥0z \geq 0.
Plain-text mathematical notation (without MathML)
Find the value of the integral ∫_(S)(∇×A)⋅da if the vector A=yi+zj+xk and S is the surface defined by the paraboloid z=1−x²−y², where z≥0.
Original LaTeX notation
Find the value of the integral $\int_S(\nabla \times \mathbf{A}) \cdot d \mathbf{a}$ if the vector $\mathbf{A}=y \mathbf{i}+z \mathbf{j}+x \mathbf{k}$ and $S$ is the surface defined by the paraboloid $z=1-x^2-y^2$, where $z \geq 0$.

category

physics

options

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

src

scibench-class

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Source and history

upstream_id / Original problem ID
9139
task_id
5d4c1b88-62cf-5280-a224-0a2f852fca4f
task_key
default--test--9139
task_revision_id
1
config / split
default / test

Official source

initial import