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            2016年成人高考專升本數學復習資料-復習指導三之一

            福建成人高考信息網www.laiwobuy.com 發布時間: 2015年11月05日

            三、一元函數積分學

            (一)不定積分

            1.知識范圍

              (1)不定積分

              原函數與不定積分的定義 原函數存在定理 不定積分的性質

              (2)基本積分公式

              (3)換元積分法

              第一換元法(湊微分法) 第二換元法

              (4)分部積分法

              (5)一些簡單有理函數的積分

            2.要求

              (1)理解原函數與不定積分的概念及其關系,掌握不定積分的性質,了解原函數存在定理。

              (2)熟練掌握不定積分的基本公式。

              (3)熟練掌握不定積分第一換元法,掌握第二換元法(限于三角代換與簡單的根式代換)。

              (4)熟練掌握不定積分的分部積分法。

              (5)會求簡單有理函數的不定積分。

            (二)定積分

            1.知識范圍

              (1)定積分的概念

              定積分的定義及其幾何意義 可積條件

              (2)定積分的性質

              (3)定積分的計算

              變上限積分 牛頓—萊布尼茨(Newton-Leibniz)公式 換元積分法 分部積分法

              (4)無窮區間的廣義積分

              (5)定積分的應用

              平面圖形的面積 旋轉體體積 物體沿直線運動時變力所作的功

            2.要求

              (1)理解定積分的概念及其幾何意義,了解函數可積的條件。

              (2)掌握定積分的基本性質。

              (3)理解變上限積分是變上限的函數,掌握對變上限定積分求導數的方法。

              (4)熟練掌握牛頓—萊布尼茨公式。

              (5)掌握定積分的換元積分法與分部積分法。

              (6)理解無窮區間的廣義積分的概念,掌握其計算方法。

              (7)掌握直角坐標系下用定積分計算平面圖形的面積以及平面圖形繞坐標軸旋轉所生成的旋轉體體積。

              會用定積分求沿直線運動時變力所作的功。

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