wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

0π/2sin3/2 xsin3/2 x+cos3/2 x dx

Open in App
Solution

Let I=0π2sinnxsinnx+ cosnxdx ... (i)= 0π2sinnπ2-xsinnπ2-x+ cosnπ2-xdx Using 0afx dx=0afa-x dx= 0π2cosnxcosnx+ sinnx dx = 0π2cosnxsinnx+ cosnx dx ... (ii)Adding (i) and (ii) we get2I =0π2sinnxsinnx+ cosnx+cosnxsinnx+ cosnx dx =0π2sinnx+ cosnxsinnx+ cosnx dx= 0π2 dx =x0π2=π2Hence I=π4i.e.,0π2sinnxsinnx+ cosnxdx=π40π2sin3/2xsin3/2x+ cos3/2xdx=π4

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Implicit Differentiation
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon