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Integral Calculus

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1 Jan 2012 08:06:12 IST

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Integral 0 to pie [tanx] [] denotes the greatest integer function

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Integral 0 to pie [tanx] [] denotes the greatest integer function

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Arjun Virmani

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Joined: 1 Jun 2009

Posts: 1294

2 Jan 2012 18:48:31 IST

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The ans is 0.

as u can see..

the integration will be done in two parts due to discontinuity at pie / 2... (90 deg)

so,

from 0 to pie/2 the function is positive.........

and from pie/ 2 to pie it is negative...........

and they are symmetric about the point (pie/2 , 0)........ !!!!

so the area above the x-axis in case 1.......will be equal to area below the x-axis in case2...and thrfr, due to about signs their sum will be nil!!!

saurav

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Joined: 30 May 2010

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7 Jan 2012 01:07:06 IST

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Ans is -pi/2. THING IS:THE SYMMETRY IS DESTROYED BY GREATEST INTEGER FUNCTION.if u see this let us see the graph,it is zero from x=0 to tan(inverse)1.if u see the same at pi end it is -1 from x=tan(inverse)-1 to pi.so sum is 0[tan(inverse)1-tan(inverse)0]-1[tan(inverse)1-tan(inverse)0].similarly 1[tan(inverse)2-tan(inverse)1]-2[tan(inverse)2-tan(inverse)1].henceforth it is -tan(inverse)n as n approaches infinity.hence -pi/2

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