1 sin 7  x c 1 14 sin 23  x 46 = 5.7 Integration using the identity Sin 3x = 3 sin x 4 sin3 x – Cos 3x = -3 cos x + 4 cos3 x Example 12 Find 6 xdx 3 Solution the identity, sin 3x = 3 sin x 4 sin3 x, – sin 18 x = 3 sin 6x 4 sin3 6 x – 3 sin 6  x 1 3 4 sin 18 x sin 6 4 x 6 xdx = 4 3 Hence 3 1 sin 18 xdx = 4 6 4 18 cos 18 3 cos 6 x x  c = 72 24 Example 13 Find 9 xdx 3 Solution Using the identity cos 3 x = - 3 cos x + 4 cos3 x Cos 27 x = 3 cos 9 x +4 cos3 9 x 3 1 cos 27 x 3 4 4 9 cos 9   x x cos Hence cos 27 3 1 xdx cos 9  xdx 9 xdx = 3
= 1 46 sin 23 x  1 14 sin 7 x  c 5.7 Integration using the identity Sin 3x = 3 sin x – 4 sin3 x Cos 3x = -3 cos x + 4 cos3 x Example 12 Find 3 6 xdx Solution the identity, sin 3x = 3 sin x – 4 sin3 x, sin 18 x = 3 sin 6x – 4 sin3 6 x sin 3 6 x  3 4 sin 6 x 1 4 sin 18 x Hence 3 6 xdx = 3 1 4 sin 18 xdx = 4 6 4 18 = cos 18 x 72 3 cos 6 x 24  c Example 13 Find 3 9 xdx Solution Using the identity cos 3 x = - 3 cos x + 4 cos3 x Cos 27 x = 3 cos 9 x +4 cos3 9 x Hence cos 3 9 x  3 4 cos 9 x  1 4 cos 27 x 3 9 xdx = 3 cos 9 xdx  1 cos 27 xdx
CALCULUS%20II.DOCX