Summary You have learnt the following from this chapter: i). The technique of integration of trigonometric expressions using the following trigonometric identities. 1 sin  x 2 1 cos 2 2 x 1. 2 1 cos  x 2. 2 1 cos 2 2 x  2 tan sec 1  x x 3. 2 2 4. cot2 x = cosec2 x - 1 5. 2 sin A cos B = sin (A + B) + sin (A B) – 6. 2 cos A cos B = cos (A + B) + cos (A B) – 7. -2 sin A sin B = cos (A+B) cos (A B) – – 8. sin 3x = 3 sin x 4 sin3 x – 9. cos 3x = -3 cos x + 4 cos3 x ii). The technique of integration using the following formulae: dx 1. 1 x  x a 2 2 tan   c a a 1 x a 2  c 2. 1 ln  x a  2 a x a dx sinh  3.  x a 2 2 x a dx if x > a  cosh 4.  x a 2 2 55 a  x if x < -a
Summary You have learnt the following from this chapter: i). The technique of integration of trigonometric expressions using the following trigonometric identities. 1. 2. sin 2 x  cos 2 x  1 2 1 2  1 2 1 2 cos 2 x cos 2 x 3. tan 2 x  sec 2 x 1 4. cot2 x = cosec2 x - 1 5. 2 sin A cos B = sin (A + B) + sin (A – B) 6. 2 cos A cos B = cos (A + B) + cos (A – B) 7. -2 sin A sin B = cos (A+B) – cos (A – B) 8. sin 3x = 3 sin x – 4 sin3 x 9. cos 3x = -3 cos x + 4 cos3 x ii). The technique of integration using the following formulae: 1. dx x 2  a 2  1 a tan x a  c 2. 1 2  1 2 a ln x a x  a  c 3. dx x 2  a 2  sinh x a 4. dx x 2  a 2  cosh x a if x > a  x a 55 if x < -a
CALCULUS%20II.DOCX