Mccarthy Edwards
07/10/2023 · Senior High School
Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field \( \mathbf{F}=5 z \mathbf{z}+2 x j+3 y k \) across the surface \( S: r(r, \theta)=r \cos \theta \mathbf{i}+r \sin \theta \mathbf{j}+\left(25-r^{2}\right) \mathbf{k}, 0 \leq r \leq 5,0 \leq \theta \leq 2 \pi \) in the direction away from the origin. The flux of the curl of the field \( F \) is (Type an exact answer, using \( \pi \) as needed.)
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The flux of the curl of the field \( F \) across the surface \( S \) is \( 50\pi \).
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