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`        integrate 0 to pi [x/(2)^(1/2)+sinx]dx`
6 years ago

SAGAR SINGH - IIT DELHI
879 Points
```										Dear student,
Expand sinx as 1-sin2x/2+sin3x/3+...
And then integrate the result..

All the best.
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Sagar Singh
B.Tech, IIT Delhi

```
6 years ago
510 Points
```										I = x/(21/2+sinx)     ..........1          lim 0 to pi

{ f(x)dx from a to b = f(a+b-x) lim from a to b  }             (property )
by using this property I becomes
I ={ (pi-x)/21/2+sin(pi-x) }dx = pi-x/(21/2+sinx)        lim 0 to pi      ............2             (sinpi-x = sinx)

2I =  {pi/21/2+sinx }dx       lim 0 to pi
now  , sinx = 2tan(x/2)/1+tan2(x/2)                   (formula)
putting this in above
2I = pi{1+tan2x/2)/(21/2+21/2tan2x/2 + 2tanx/2) dx          lim 0 to pi
1+tan2x/2 = sec2x/2                  (formula)
2I = pi{sec2x/2/(21/2 +21/2tan2x/2 + 2tanx/2) }          dx lim 0 to pi
now put tanx/2 =  t   then  , sec2x/2dx = 2dt
2I ={ 2pi/(21/2+21/2t2+2t) } dt          lim 0 to infinity
I = pi/21/2 . {1/t2+21/2t+1} dt           lim 0 to infinity
now this becomes simple integral and u can easily proceed now...

approve if u like it
```
6 years ago
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