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第十四單元 弧長與旋轉體的表面積
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Length of a Plane Curve
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Example
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Example(continued)
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Review of the Arc Length Formula
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Example
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Example(continued)
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Example(continued)
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Area of a Surface of Revolution
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Area of a Surface by a strip
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Surface Area Formula
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Example Find the surface area of the surface generated by revolving
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Example Find the surface area of the surface generated by revolving
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Example(continued)
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Example Find the surface area of the surface generated by revolving
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Example(continued)
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單元結語 曲線的弧長公式看起來簡單又對稱，但實際積分將會發現非常難以積分，例如橢圓的弧長所造成的橢圓積分只能計算近似值，真值是無法以初等函數的型態表達。 旋轉體的表面積也是一樣，能計算出來的例子很少，故本單元以介紹觀念為主要目的。
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