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22-05-2023
Mathematics

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Let M be the capped cylindrical surface which is the union of two surfaces, a cylinder given by x^2+y^2=36, 0≤z≤1, and a hemispherical cap defined by x^2+y^2+(z−1)^2=36, z≥1. For the vector field F=(zx+z^2y+7y, z^3yx+8x, z^4x^2), compute ∬M(∇×F)⋅dS in any way you like.

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