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求平面图形的面积是定积分在几何中的重要应用,把求平面图形的面积问题转化为求定积分问题,充分体现了数形结合的数学思想。下面例析用积分求面积时两种常用的解题技巧。一、巧选积分变量求平面图形的面积时,要注意选择积分变量,可使计算简捷。例1,求抛物线y~2=2x与直线y=x-4围成的平面图形的面
The area of the plane graphic is an important application of the definite integral in the geometry. The area problem of the plane graphic is transformed into the problem of determining the integral, which fully embodies the mathematics thought of the combination of the number and the shape. The following example uses integrals to find two common problem solving techniques. A, select the integral variables When calculating the area of plane graphics, pay attention to select the integral variables, can make the calculation simple. Example 1, find the parabola y ~ 2 = 2x and the line y = x-4 surrounded by the surface of the plane graphics