CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
Question

Integrate sinx+cosxsin2x

Open in App
Solution

Let I=sinx+cosxsin2xdx
Let sinxcosx=t
(cosx+sinx)dx=dt
Further t2=(sinxcosx)2=sin2x+cos2x2sinxcosx
t2=12sinxcosx
2sinxcosx=sin2x=1t2
I=dt1t2dx
=sin1t+c where c is the constant of integration.
=sin1(sinxcosx)+c
Since sinxcosx=2(12sinx12cosx)
=2(cosπ4sinxsinπ4cosx)+c
I=2sin(xπ4)+c

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Property 7
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon