what am I doing wrong in this trig integration question? (1 Viewer)

[SureBluff]

for the sake of convenience, I'll call the integration sign ... (you know, the sign that looks like a giant 'f' or distorted 's')

find primitive of (sinx)^2

(sinx)^2dx
=1/2(1-cos2x)dx
=1/2(1-cosu)(1/2du)
=1/4(x-sin2x)+C

the answer at the back of the book was (1/2)x-(1/4)sin2x+C
I dunno where I went wrong, help!!!

 

[shafqat]

for the sake of convenience, I'll call the integration sign ... (you know, the sign that looks like a giant 'f' or distorted 's')

find primitive of (sinx)^2

(sinx)^2dx
=1/2(1-cos2x)dx
=1/2(1-cosu)(1/2du)
= 1/4(u - cosu)
= 1/4(2x - sin2x)
= x/2 - 1/4 sin2x + C
the answer at the back of the book was (1/2)x-(1/4)sin2x+C
I dunno where I went wrong, help!!!

.......................

 

[renya]

=1/2(1-cosu)(1/2du)

your right up to this line
then u get
=1/4 (1 - cos u) du
=1/4 [u - sin u ] + C
=1/4 [2x - sin 2x] + C
=(1/2)x - (1/4)sin 2x + C

 

[SureBluff]

*slaps forehead* aghhh

thanks Renya, forgot the substitution.