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[Post New] 14 Nov 2009 21:57:31 IST
   Subject: Integrate
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Deepak Aggarwal (3759)

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Integrate [x] f'(x) limit from 1 to a, where a>1 and [.] represents the greatest integer function
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[Post New] 14 Nov 2009 22:16:37 IST
   Subject: Integrate
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Yagyadutt Mishra (5432)

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[Post New] 14 Nov 2009 22:57:54 IST
   Subject: Integrate
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Bipin Dubey (13659)

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I=\int_{1}^{2}[x]f'(x)dx+\int_{2}^{3}[x]f'(x)dx+.....+\int_{[a]}^{a}[x]f'(x)dx

 

I=\int_{1}^{2}1f'(x)dx+\int_{2}^{3}2f'(x)dx+.....+\int_{[a]}^{a}[a]f'(x)dx

 

I=1(f(2)-f(1))+2(f(3)-f(2))+.....+[a](f(a)-f([a]))

 

I=[a]f(a)-(f(1)+f(2)+f(3)+......+f([a]))

 

 
Bipin Kumar Dubey
Chemical Dept.
IIT Kharagpur

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