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![[Post New]](/templates/default/images/icon_minipost_new.gif) 19 Nov 2006 21:45:14 IST
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SINCE, 0 ] [1 ] f(x) dx = 1, [0 ] [ 1] xf(dx) = a & [0 ] [ 1] x 2 f(x) dx a 2, therefore, I = [0 ] [ 1] (a -x) 2f(x) dx is = [0 ] [ 1] (a 2 - 2ax + x 2)f(x) dx or I = [0 ] [ 1] a 2 f(x) dx -2a [0 ] [ 1] x f(x) dx + [0 ] [ 1] x 2f(x) dx or I = a 2 [0 ] [ 1] f(x) dx - 2a(a) + a 2 = a 2.1 - 2a.a + a 2 so, I = 0
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The Scientist does not study nature because it is useful; he studies it because he delights in it, & he delights in it because it is beautiful. If nature were not beautiful, it would not be worth knowing, life would not be worth living. Ofcourse I do not here speak of that beauty that strikes the senses, the beauty of qualities & appearances; not that I undervalue such beauty, far from it, but it has nothing to do with science; I mean that profounder beauty which comes from the harmoniuos order of the parts, & which a pure intelligence can grasp. |
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