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The definition of abnormal points on Some Thoughts

egrationaregiveninthispaper. Keywordsinfinilionintegration; non-normalinlegration; limit; convergence; divergence. Non-normal points to determine the definition of live abnormal integral convergence and divergence plays an important role. But if we carefully study the definition of coast, you will find there is still a place in the definition of serious loss. This paper [1], for example, a few observations. Definition 1 Let the function f defined in the infinite I asked [n, + ∞), and in any finite interval [Ⅱ, A] can be integrated if the limit, 4liraJ. Plant =_,,( 1) A-Ten ∞ J + ∞ l, = J_ factory () dx or J / ', J If the limit (1) does not exist, called infinite limit of J in the Introduction: Li r port J Lee (1976 a), female, teaching assistants, mainly in higher mathematics teaching for A] concentration as that,: 0,[link widoczny dla zalogowanych],1 imf plant: 0,[link widoczny dla zalogowanych], J Ⅱ,, ... J ¨, by definition, If convergence. In this case, Il 『'only that it functions in a convergent, infinite storage area instead of asking [a, + ∞) convergence. Therefore, the values of A Fan Si provisions of A> a better. 2 definition itself misleading, said the first part of the definition of the meaning of integration is not J ¨ breaks. Infinite integral only refers to the integration interval is infinite limit points, then, whether (1) the existence of the limit infinite integral can be called, and when (1) the limit exists, only that Jf convergence, when Ja ( 1) The limit does not exist, only that J / divergence. L7 Tarim Volume 3 of the first definition of function in [0, + ∞) the continuous or did not specify the definition of not continuous, there is discontinuity point c, we can always find a closed interval [n,[link widoczny dla zalogowanych], C], so c included, in which, J / to be improper integrals, the problem becomes complex. However, in fact the definition of J Ⅱ _ 1 is the default factory in [, + o. ) Is continuous. Given the above understanding, we define an appropriately modified as follows: Definition l setting function / as defined in the infinite interval [t /,, + o. ) A continuous function, and in any finite interval [t /,, A] can be integrated. Remember. 1imf =',(', can be limited, but also for infinite) - Ten ∞ J Ⅱ called the limit 'for the function in [, + o. ) Infinite limits on non-normal points (or simply infinite integral), denoted by, + ∞, + ∞ ', = I-Plant () dx or I /, d (1d (1 if l, called finite I, convergence, the J is infinite, called Infinite ∞ limit of ten sub-plot d f / divergence. Similarly, we can modify (a ∞,[link widoczny dla zalogowanych], b] on the infinite integral. For non-normal points of unbounded functions, there is similar to the definition of a 2,3 issues, so we can be modified as follows: Definition 2 defined in the [mouth, b) _ a continuous function on the plant, at the point b, no industry left the area, and accounted for any positive number (<b A ) in the [mouth, b-s] can be integrated, and mind., 6 a IiIf = G (G can be finite, but also for infinite) ,8-u dO called the limit of ten unbounded function of non-normal points , denoted rbrb ', = I) dx Wei I /, dt2J limited oral b if G called abnormal integral unbounded function f, convergence, if G is Ja, b infinite, unbounded function called abnormal integral J / divergence. Ja Similarly, we can modify (port, b] unbounded function on the non-normal points.

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