1. Let D be the region bounded by the parabola y = x² - x and the x-axis. Find the slope of the line passing through the origin that divides D into two regions with equal area.__(a)__

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Chia Chung

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2024/09/20

<Solution>6 ...

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2. (10 分) Let C be a positively oriented, piecewise-smooth, simple closed curve in the plane and let D be the region bounded by C. If f(x, y) is a scalar function with continuous first and second partial derivatives in D, derive the following formula: ∬D ( fxx + fyy )dxdy =where = ∇f⋅N is the normal derivative, N is an outer unit normal, s is the arc-length.

1. Let D be the region bounded by the parabola y = x² - x and the x-axis. Find the slope of the line passing through the origin that divides D into two regions with equal area.(a)

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