Need help FAST within 12 hrs- Techniques of Integration, 1 question,?

Question

Can someone please tell me where ¼ is coming from, FAST PLEASE!!!!!!


∫sin2 x dx
=∫ 1-cos 2x/2 dx
=½ ∫ dx -1/2 ∫cos 2x dx
=1/2x -1/4sin 2x +c

Answer 1

Writing this out in more detail:
1/2 ∫cos (2x) dx
u=2x, du=2 dx, dx=du/2
1/2 ∫cos u/2 du
1/4 ∫cos u du
1/4 sin u + C
1/4 sin (2x) + C

The u comes from the fact that you are integrating cos 2x, not cos x.

Oh, and in the second step, you should have ∫(1-cos (2x))/2 dx -- the way you wrote it literally means ∫1 - x (cos 2)/2 dx, which is absurd.

Answer 2

the quintessential of cos2x is a million/2 sin2x (it somewhat is straight forward to envision, merely paintings out the spinoff of a million/2 sin2x and you get cos 2x) so this a million/2 alongside with the a million/2 outdoors the quintessential grants a million/4 desire this facilitates!