4. Find the area of the surface generated by revolving the cardioid r = 1 + cosθ around the x-axis. __(d)__

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Chia Chung

詳解 #6218834

2024/09/29

<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.

4. Find the area of the surface generated by revolving the cardioid r = 1 + cosθ around the x-axis. (d)

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