Trig Integrals (Even Powers of Sine and Cosine)

This calculus tutorial video on trig integrals shows you how to integrate even powers of sine and cosine functions using identities. We have several step-by-step worked examples of integrating even powers of sine and cosine functions, with an explanation of the overall method of using double-angle identities at the beginning of the video. We show examples of integrating an even power of sine, even power of cosine, and a combination of sine and cosine functions where all powers are even. Trigonometric integrals are a common topic found in a Calculus 2 or AP Calculus course.
0:00 The method used
1:19 Example 1
2:32 Example 2
3:46 Example 3
7:47 Example 4

[Jonny-opwr]

I understand why you have 1/2 combined with 1 but i dont understand why its 1/2 cos 4x can you elaborate. The video section is 6:36.