Refer to http://hk.knowledge.yahoo.com/question/?qid=7007101004674
∫u2 dx
=∫u2/(2x) du
dx is changed to du/(2x)
that means we treat dx as a algebraic term? I’ve just learn integration, isn’t du a part of the whole notation?
to me, it’s very strange to change dx to du/(2x) as I think
dx is a part of the integration notation
concept of integration by substitution(2)
2007-10-11 7:19 am
回答 (1)
2007-10-11 8:11 am
✔ 最佳答案
yes, u're right. The theorem of integration by substitution is treated vigorously in Pure Maths. But in Amaths, we adopt the "easy calculation" approach, it treat the symbol dx and ∫ in separate form.
The original theorem should be as follow:
If f is a function u, and u is function of x (continuity, differentiable are neglected in this version), then
∫f(u(x)) u'(x) dx = ∫ f(u) du
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