Find an anti derivative (or integral) of the following functions by the method of inspection. 1. sin 2x 2. cos 3x 3. e 2x 4. (ax + b) 2 5. sin 2x 4 e 3x Find the following integrals in Exercises 6 to 20: 6. 3 (4 + 1) x e dx 7. 2 2 1 x (1 ) dx x 8. 2 ( ) ax bx c dx 9. 2 (2 ) x x e dx 10. 2 1 x dx x 11. 3 2 2 x x 5 4 dx x 12. 3 x x3 4 dx x 13. 3 2 1 1 x x x dx x 14. (1 ) x x dx 15. 2 x( 3 2 3) xxd x 16. (2 3cos ) x x xed x 17. 2 (2 3sin 5 ) x x xd x 18. sec (sec tan ) x x x dx 19. 2 2 sec cosec x dx x 20. 2 2 3sin cos x x dx. Choose the correct answer in Exercises 21 and 22. 21. The anti derivative of 1 x x
Find an anti derivative (or integral) of the following functions by the method of inspection.
Question 1:sin 2x
Question 2:cos 3x
Question 3:e 2x
Question 4:(ax + b) 2
Question 5:sin 2x – 4 e 3x Find the following integrals in Exercises 6 to 20:
Question 6:3 (4 + 1) x e dx
Question 7:2 2 1 x (1 – ) dx x
Question 8:2 ( ) ax bx c dx
Question 9:2 (2 ) x x e dx
Question 10:2 1 x – dx x
Question 11:3 2 2 x x– 5 4 dx x
Question 12:3 x x3 4 dx x
Question 13:3 2 1 1 x x x– dx x –
Question 14:(1 ) – x x dx
Question 15:2 x( 3 2 3) xxd x
Question 16:(2 3cos ) x x – xed x
Question 17:2 (2 3sin 5 ) x – x xd x
Question 18:sec (sec tan ) x x x dx
Question 19:2 2 sec cosec x dx x
Question 20:2 2 – 3sin cos x x dx. Choose the correct answer in Exercises 21 and 22
Question 21:The anti derivative of 1 x x equals (A) 1 1 3 2 1 2 C 3 x x (B) 2 2 1 3 2 C 3 2 x x (C) 3 1 2 2 2 2 C 3 x x (D) 3 1 2 2 3 1 C 2 2 x x
Question 22:If 3 4 3 () 4 d fx x dx x such that f (2) = 0. Then f (x) is (A) 4 3 1 129 8 x x (B) 3 4 1 129 8 x x (C) 4 3 1 129 8 x x (D) 3