By using the properties of definite integrals, evaluate the integrals in Exercises 1 to 19. 1. 2 2 0 cos x dx 2. 2 0 sin sin cos x dx x x 3. 3 2 2 3 3 0 2 2 sin sin cos x dx x x 4. 5 2 5 5 0 cos sin cos x dx x x 5. 5 5 | 2| x dx 6. 8 2 x 5 dx 7. 1 0 (1 )n x x dx 8. 4 0 log (1 tan ) x dx 9. 2 0 x 2 x dx 10. 2 0 (2log sin log sin 2 ) x x dx 11. 2 2 2 sin x dx 12. 0 1 sin x dx x 13. 2 7 2 sin x dx 14. 2 5 0 cos x dx 15. 2 0 sin cos 1 sin cos x x dx x x 16. 0 log (1 cos ) x dx 17. 0 a x dx x a x 18. 4 0 x 1 dx 19. Show that 0 0 ()()
By using the properties of definite integrals, evaluate the integrals in Exercises 1 to 19
Question 1:2 2 0 cos x dx✁
Question 2:2 0 sin sin cos x dx x x
Question 3:3 2 2 3 3 0 2 2 sin sin cos x dx x x
Question 4:5 2 5 5 0 cos sin cos x dx x x
Question 5:5 5 | 2| x dx
Question 6:8 2 x 5 dx
Question 7:1 0 (1 )n x x dx
Question 8:4 0 log (1 tan ) x dx
Question 9:2 0 x 2 x dx
Question 10:2 0 (2log sin log sin 2 ) x x dx
Question 11:2 2 – 2 sin x dx ✓ ✔ ✓
Question 12:0 1 sin x dx x ✕ ✖ ✗
Question 13:2 7 – 2 sin x dx ✓ ✔ ✓
Question 14:2 5 0 cos x dx ✘
Question 15:2 0 sin cos 1 sin cos x x dx x x
Question 16:0 log (1 cos ) x dx ✘
Question 17:0 a x dx x a x
Question 18:4 0 x 1 dx
Question 19:Show that 0 0 ()() 2 () a a f x g x dx f x dx ✚ , if f and g are defined as f(x) = f(a – x) and g(x) + g(a – x) = 4 Choose the correct answer in Exercises 20 and 21
Question 20:The value of 2 3 5 2 ( c x xx xd os tan 1) x ✓ ✛✓ ✜ ✜ ✜ ✔ is (A) 0 (B) 2 (C) ✢ (D) 1
Question 21:The value of 2 0 4 3 sin log 4 3 cos x dx x ✣ ✤ ✥ ✩ ✪ ✫ is (A) 2 (B) 3 4 (C) 0 (D)
