一类原函数的面积求法

在几何上,定积分可简单地描述为曲边梯形的面积.在积分区间内,被积函数对应的曲线所围成的几何区域如为圆和矩形等一些容易计算面积的规则图形时,就可以通过计算图形面积来计算相应的定积分.这样可以免去一些复杂的计算过程.把定积分的面积计算法应用于上限积分的函数,利用上限积分的函数与原函数间的关系,得到所需求的原函数.在应用过程中发现,参数方程形式的选取对计算有着一定的影响.

The area method for a kind of original function

The definite integral can be simply expressed as the area of the trapezoid with curve sides based on the geometric points. In integrating range, if the zone enclosed by the integrating function is rectangle or circle whose area can be computed easily, the corresponding integral can be ascertained by the area of the zone. By doing so, some complicated computation process can be deleted. The area method was applied on the upper limit integral functions. By the relationship between the upper limit integral functions and the original function, the original function can be expressed. In the application, it is found that the parameter equation plays important role in the computation.