
evaluate the surface integral. s x2z + y2z ds s is the hemisphere x2 + y2 + z2 = 9, z ≥ 0
 Mathematics

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miramckinney841  1 month ago

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The surface integral is equal to the volume of the hemisphere. Integral S x2z + y2z ds = ∫∫ (x2z + y2z)dA = ∫∫r2sin θ zdθdφ = (1/3)∫π/2 0 ∫2π 0 r6sin3 θ dφdθ = (1/3)(4π/3)(9^3/3) = 36π

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Colby Whitaker

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The surface integral is ∫s x2z + y2z ds, where s is the hemisphere x2 + y2 + z2 = 9, z ≥ 0. Using the formula of a hemisphere and converting the integral to polar coordinates, we get: ∫s x2z + y2z ds = ∫0 (9  r2)r2*z drdθ Integrating with respect to r and θ yields: ∫s x2z + y2z ds = 9π/4

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Juliana Neal

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