Guest

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

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

Grade:12

2 Answers

SAGAR SINGH - IIT DELHI
878 Points
13 years ago

Dear student,

Expand sinx as 1-sin2x/2+sin3x/3+...

And then integrate the result..

Please feel free to ask your queries here. We are all IITians and here to help you in your IIT JEE preparation.

All the best.

Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.

Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar  respectively : Click here to download the toolbar..

 

Askiitians Expert

Sagar Singh

B.Tech, IIT Delhi

vikas askiitian expert
509 Points
13 years ago

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)

adding 1 & 2

 

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

Think You Can Provide A Better Answer ?

ASK QUESTION

Get your questions answered by the expert for free