Definite integration
本帖最後由 數學小子 於 1-1-2011 12:27 編輯1)in(0 to 1)x^m(1-x)ndx
2)lim(x->inf.)t^2dt]2/2)etdt] 1)
Lethttp://upload.wikimedia.org/math/c/d/b/cdb20e0a02114aed249bf4d7005389f7.png
http://upload.wikimedia.org/math/1/3/f/13f4171eb76c530bbcfc30400e90a63c.png
http://upload.wikimedia.org/math/7/f/9/7f9099ca3a5c6399b8a328ca4d435c95.png
http://upload.wikimedia.org/math/7/5/9/7592b46cced3ff582ca9c1719cada837.png,
It's not hard to imagine that
http://upload.wikimedia.org/math/1/8/3/183ef34964339b4faa13495fdcdc6b34.png,
http://upload.wikimedia.org/math/6/d/2/6d297400060b950f310ac3163f807a1b.png
http://upload.wikimedia.org/math/d/9/d/d9dbbb706f0dbe16d4124a445cdf2041.png
http://upload.wikimedia.org/math/c/5/d/c5d17a4262916f6dfefc21e04e18fc22.png
2)
This is an http://upload.wikimedia.org/math/2/6/e/26ea0473a6b118c9e3bad5b0337f78e2.png case, therefore L'Hospital rule is used
http://upload.wikimedia.org/math/c/0/4/c04d23f90d2e23a5d6c379bea0231814.png
http://upload.wikimedia.org/math/5/6/1/561d4da6351a9ba4b8841fb041bdc65e.png
http://upload.wikimedia.org/math/9/d/a/9da7ebf90d03a59b2f19055d3d9f37d2.png
it's still http://upload.wikimedia.org/math/2/6/e/26ea0473a6b118c9e3bad5b0337f78e2.png, L'Hospital rule is used again
http://upload.wikimedia.org/math/d/8/a/d8a5d54c174df0e81d7d8db1a1bac71d.png
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