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![[Post New]](/templates/default/images/icon_minipost_new.gif) 9 Apr 2008 20:08:59 IST
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f(x) = tanx - tanx tanx tanx +tanx tanx tanx tanx tanx+..................+ infinity 0 less than x less than 45 degrees then [0 ] [ /4 ] f(x) dx =
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9 Apr 2008 20:14:14 IST
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is it 1/4
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9 Apr 2008 20:17:52 IST
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tell me hw to solve this problem
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9 Apr 2008 20:18:43 IST
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sunip tell me hw did u solve the sum
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9 Apr 2008 20:23:24 IST
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i think the answer should be
-1/4
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9 Apr 2008 20:23:25 IST
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it is infinite g.p. with common difference -tan2x.
now sum of the g.p. will be tanx/1+tan2x
which is equal to sinxcosx....now u can integrate it easily
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9 Apr 2008 20:25:41 IST
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sunip can u explain it more briefly
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9 Apr 2008 20:25:49 IST
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i am getting -1/4
f(x) = sinx cosx
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9 Apr 2008 20:32:46 IST
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sunip tell me hw did u find the sum of gp
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9 Apr 2008 20:35:45 IST
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the sum of GP can be found by using the summation formula of infinite terms
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9 Apr 2008 20:36:08 IST
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its the sum of an infinite g.p.the formula is as follows..
s=a/1-r;a=first term ,r=common difference ,|r|<1
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9 Apr 2008 20:46:03 IST
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even iam getting -1/4 but the right ans is 1/4 what to do sunip
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10 Apr 2008 10:54:52 IST
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hey ans is 1/4. ......... i think u all r doing mistake in integration of sin, it is -cos rate me please
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10 Apr 2008 11:59:01 IST
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Q) f(x) = tanx - tanx tanx tanx +tanx tanx tanx tanx tanx+..................+ infinity 0 less than x less than 45 degrees then [0 ][/4 ] f(x) dx = ? Sol) Let y =f(x) = tanx - tanx tanx tanx +tanx tanx tanx tanx tanx+............... Thus y = tanx -tan2 x ( tanx - tanx tanx tanx +tanx tanx tanx tanx tanx+....) or y = tanx - y tan2 x or y + y tan2 x = tanx or y = tanx / (1 + tan2 x) or y = sinx cosx = (sin2x)/2 Thus, I = [0 ][/4 ] f(x) dx or I =[0 ][/4 ] y dx or I = [0 ][/4 ] sin2x / 2 dx or I = -(1/4)(cos/2 - cos0) = 1/4
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