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CBSE Class 11-science Answered

integration
Asked by Kirandoon | 07 Jan, 2009, 02:06: PM
answered-by-expert Expert Answer

write cos 2x as 1 - 2sin2x  so we get numenator of above expression as 2sin2x - (1 - cosx)  so the final expression is  sin2x / sin2x/2 - 1 (as 1 - cosx = 2 sin2(x/2))

as sin 2a = 2 sin a cos a  so sin2x  = { 2 sin (x/2) cos (x/2) } 2 = 4 sin 2(x/2) cos2 (x/2)

so final integration term is  4 cos2 (x/2)  - 1  = 2(1 + cos x)  - 1  = 2cos x + 1 

so answer is 2 sinx + x

Answered by | 12 Jan, 2009, 07:59: PM

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