# 积分

integral

accumulate points

this article discusses the integral theorem of mean the promoted question, mainly has two aspects: On the one hand in analyzes in the teaching material under the first integral theorem of mean condition, had proven lies between the value spot to have to be possible to obtain in the open-interval, further discusses this knot promotes to the generalized Riemann integral, and further proved the conclusion also establishes to the promoted first integral theorem of mean; Promotes on the one hand in addition the integral theorem of mean to in the curve and the curved surface, and has proven the curvilinear integral theorem of mean and the surface integral theorem of mean.

Then the boundary element integral equation of interior and exterior form is deduced in detail, also the form with corner coefficient. The significance for numerical calculation and principle of the singular integral is analyzed, and a non-isoparametric transformation method is presented to calculate weak singular integral and Cauchy integral, the method presented provides us a very simple way to computer the two kinds of singular integral of Helmholtz boundary integral equation, and it is easy to program in computer. After the difficulty of the calculation for multi-frequency of Helmholtz boundary element is explained, a method named SECHIEF (Series Expansion Combined Helmholtz Integral Equation Formulation), which is focused on the computational efficiency, is presented.

By means of traditional criterions of generalized integral's convergence and divergence, this paper, from the analysis of integrated function's nature, discovers a series of new criterions, which are briefer and more suitable: on the aspect of generalized integral for functions of a single variable, through the investigation of integrated function, together with the inner relationship between positive series and generalized integral in infinite interval under the condition of positive function, it gives several criterions of generalized integral's convergence and divergence, which are similar to positive series' criterions of convergence and divergence.

Indefinite integral concept,, indefinite integral nature of the basic integral formula, the indefinite integral proofs, indefinite integral substitution integration, integration by parts, the indefinite integral rational function integral.

Indefinite integral concept,, indefinite integral nature of the basic integral formula, the indefinite integral proofs, indefinite integral substitution integration, integration by parts, the indefinite integral rational functions.

JuJu 积分+2 Happy Birthday!

The objective of this study is aimed at the implementation of parallelized numerical quadrature routines. The algorithm we choose for numerical quadrature routines is the so called "Adaptive Romberg Tree integration scheme"(abbr."ARTint") proposed by Lin et. al.[1997]. This numerical quadrature scheme can arrange the function evaluation points adaptively in accordance with characteristic of the trend of variation in integrand function values. When the accuracy of the numerical quadrature value is requested to be increased, a newer and larger set of function evaluation points must be incurred. The main advantage of ARTint method is the inclusion of all function evaluation points used in previous stages. It is this feature of ARTint method that makes it a quadratue scheme with prominent computation efficiency.

After the unrated player chooses a rated player on the ladder and arranges with him/her an Initial Rating Match: a if the unrated player wins 3-0, he/she will receive the rating of the rated player plus 50 points; if wins 3-1 plus 25; if wins 3-2 plus 10; c if the unrated player loses 2-3 he/she will receive a rating 50 points lower then the rated player but not below the rating of the lowest player on the ladder; if 1-3 he/she will receive a rating 100 points lower then the rated player but not below the rating of the lowest player in the ladder; if 0-3 he/she will receive a rating 200 points lower then the rated player but not below the rating of the lowest player in the ladder.

The results show that mechanical heterogeneity has great influence on the J-integral of welded joint containing transverse crack. The J-integral on the path cross the interface between welded joint and base metal is higher than the J-integral on the paths in the weld metal for undermatched joint,while the J-integral on the path cross the interface between weld metal and base metal is lower than the J-integral on the paths in the weld metal for overmatched joint. Moreover,the difference of J-integral values increases with the increasing of the load and strength mismatching difference and the path-enclosed length of interface between weld metal and base metal.

Conditions of integral chain can be closed.

integral action：积分动作,积分作用

1468. integral 积分,总体,整体,集成 | 1469. integral action 积分动作,积分作用 | 1470. integral action coefficient 积分作用系数,积分动作系数

integral action coefficient：积分作用系数,积分动作系数

1469. integral action 积分动作,积分作用 | 1470. integral action coefficient 积分作用系数,积分动作系数 | 1471. integral action control 积分动作控制

Improper integral：瑕积分

surface integral：面积分

Integrating factor：积分因数,积分因子=>積分因子

integrating exposure meter 积分曝光计 | integrating factor 积分因数,积分因子=>積分因子 | integrating filter 积分滤波器

integration by parts：部分积分法;分部积分法

integration by substitution：代换积分法;换元积分法

integration by parts 分部积分法 | integration by substitution 代换积分法;换元积分法 | integration constant 积分常数

line integral：线积分

line integral：曲线积分

Windup protection：积分饱和防护,抗积分饱和