Evaluate
1.Integarl 0 to pi ((xtanx)dx/(secx+tanx))
​2. Integral 0 to pi/2 ((xsinxcosx)dx/(sin4x+cos4x)

Dear Student,
Please find below the solution to the asked query:

I=0πx.tanxsecx+tanx.dx.....i=0πx.sinxcosx1cosx+sinxcosx.dx=0πx.sinxcosx1cosx+sinxcosx.dxI=0π x.sinx1+sinx.dxUse 0afx.dx=0afa-x.dxI=0π π-x.sinπ-x1+sinπ-x.dx=0π π-x.sinx1+sinx.dxI=π0πsinx1+sinx.dx-0πx.tanxsecx+tanx.dxUsing i we getI=π0πsinx1+sinx.dx-I2I=π0πsinx1+sinx.dx2Iπ=0π1+sinx-11+sinx.dx2Iπ=0π1+sinx1+sinx.dx-0π11+sinx.dx2Iπ=0π1.dx-0π11+sinx1-sinx1-sinx.dx2Iπ=x0π-0π1-sinx1-sin2x.dx2Iπ=π-0-0π1-sinxcos2x.dx2Iπ=π-0π1cos2x-sinxcos2x.dx2Iπ=π-0πsec2x-sinx.tanx.dx2Iπ=π-tanx-secx0π=π-0--1-0-1=π-1+12Iπ=π-2I=ππ-22Please ask one question in one thread. 

Hope this information will clear your doubts about this topic.

If you have any doubts just ask here on the ask and answer forum and our experts will try to help you out as soon as possible.
Regards

  • -1
What are you looking for?