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Integral of xsinx/(1-cosx ) over 0 to pi Evaluate above integral problem

2 years ago

Answers : (2)

25285 Points
Dear Javed
 => write sinx and cosx in half angle formulaes:
=> (x + 2sinx/2cosx/2)/(2cos^2x/2)dx => 0.5xsec^2x/2 dx + tanx/2 dx …..........................(1)

let tanx/2 = u
0.5sec^2x/2 dx = du
and x = vv
dx = dv
substittue in the eqn. (1)
and after integrating we get,
=> xtan(x/2) + c
2 years ago
Aditya Gupta
2069 Points
Put x=2y integral becomes
4*∫0 to pi/2 ycoty dy
Integrate by parts taking first function as y.
y*lnsiny|0 to pi/2 - ∫0 to pi/2 lnsiny dy
= 0 -0 - (-pi ln2)/2
= (πln2)/2
Note that integral of lnsinx from 0 to pi/2 is -piln2/2 (it's a solved ncert example) san also limit y tends to zero ylnsiny is equal to zero
2 years ago
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