Sum versus integration illustrated in 3D for z = sin(x) sin(y) on [0,π]×[0,π]. Discrete volume elements give ∑ ΔA sin(x) sin(y) ≈ 4.0008, matching the exact double integral ∫₀^π ∫₀^π sin(x) sin(y) dy dx = 4.

Name: Sum versus integration illustrated in 3D for z = sin(x) sin(y) on [0,π]×[0,π]. Discrete volume elements give ∑ ΔA sin(x) sin(y) ≈ 4.0008, matching the exact double integral ∫₀^π ∫₀^π sin(x) sin(y) dy dx = 4.
Channel: Matheorems
Description: Sum versus integration illustrated in 3D for z = sin(x) sin(y) on [0,π]×[0,π]. Discrete volume elements give ∑ ΔA sin(x) sin(y) ≈ 4.0008, matching the exact double integral ∫₀^π ∫₀^π sin(x) sin(y) dy dx = 4.

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Sum versus integration illustrated in 3D for z = sin(x) sin(y) on [0,π]×[0,π]. Discrete volume elements give ∑ ΔA sin(x) sin(y) ≈ 4.0008, matching the exact double integral ∫₀^π ∫₀^π sin(x) sin(y) dy dx = 4.

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