英语
摘要:本文简要的阐述定积分在几何、物理以及初等数学等方面的应用.在这一部分,主要采用了“微元法”这一思想理论来解决实际中的问题.定积分是分布区间上的整体量.因为整体是由局部组成,所以将实际问题抽象为定积分,必须从整体着眼,从局部入手.譬如,在求不规则曲边四边形的平面区域面积时,我们往往将其转化为积分问题,从而达到解题的目的.(先求曲边四边形的面积微元 ,在区间 上任取一点x,在点x上的面积微元 ,就是“高”为f(x),宽为微分 的矩形面积,即 .(矩形面积=高×宽)又例如,利用定积分求x=5cost,y=

2019-04-15

摘要:本文简要的阐述定积分在几何、物理以及初等数学等方面的应用.在这一部分,主要采用了“微元法”这一思想理论来解决实际中的问题.
定积分是分布区间上的整体量.因为整体是由局部组成,所以将实际问题抽象为定积分,必须从整体着眼,从局部入手.譬如,在求不规则曲边四边形的平面区域面积时,我们往往将其转化为积分问题,从而达到解题的目的.(先求曲边四边形的面积微元 ,在区间 上任取一点x,在点x上的面积微元 ,就是“高”为f(x),宽为微分 的矩形面积,即 .(矩形面积=高×宽)又例如,利用定积分求x=5cost,y=4sint的椭圆曲线的周长以及立体体积等等,并简要的论述了定积分在物理中的简单应用,也简单的介绍了定积分在初等数学中的基本运用.
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Abstract: This article briefly describes the definite integral in geometry, physics and elementary mathematics and other applications. In this section, the main use of the "micro-element method," the idea in theory to solve practical problems.
Distribution range of the definite integral is the overall volume. Because the overall composition by local, so the actual problem is abstracted as the definite integral, we must focus on the whole, from the local start. For example, in seeking irregular curved quadrilateral plane size of the area, we tend to be translated into the problem points to achieve the purpose of solving problems. (First find the area of micro-curved quadrilateral element, in the range of office to take a little x, at point x on the area of micro-yuan, is "high" for the f (x), width of the rectangular area of the differential, that is. (Rectangular area = height × width) another example, the use of fixed points find x = 5cost, y = 4sint the perimeter of the elliptic curve, and three-dimensional volume, etc., and a brief discussion of the definite integral of a simple application in physics, but also a brief introduction the definite integral in the basic use of elementary mathematics.
Abstract: This article briefly describes the definite integral in geometry, physics and elementary mathematics and other applications. In this section, the main use of the "micro-element method," the idea in theory to solve practical problems.
Distribution range of the definite integral is the overall volume. Because the overall composition by local, so the actual problem is abstracted as the definite integral, we must focus on the whole, from the local start. For example, in seeking irregular curved quadrilateral plane size of the area, we tend to be translated into the problem points to achieve the purpose of solving problems. (First find the area of micro-curved quadrilateral element, in the range of office to take a little x, at point x on the area of micro-yuan, is "high" for the f (x), width of the rectangular area of the differential, that is. (Rectangular area = height × width) another example, the use of fixed points find x = 5cost, y = 4sint the perimeter of the elliptic curve, and three-dimensional volume, etc., and a brief discussion of the definite integral of a simple application in physics, but also a brief introduction the definite integral in the basic use of elementary mathematics.
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