Integrals
5/2 / 5 50 / cos / sin cos x dx x x π +∫ 5. 5/5 | 2 |x dx − +∫ 6. 8/2 5x dx−∫
1/0 (1 ) nx x dx−∫ 8. 4 log (1 tan )x dx π +∫ 9. 2/0 2x x dx−∫ 10. 2 (2log sin log sin 2 )x x dx π −∫ 11. 2 2 - sin x dx π π∫ 12. 0 1 sin x dx x π +∫ 13. 7 2 - sin x dx π π∫ 14. 2 5 cos x dx π ∫ 15. 2 sin cos 1 sin cos x x dxx x π − +∫ 16. log (1 cos )x dx π +∫ 17. 0 a x dx x a x+ −∫ 18. 4/0 1x dx−∫ 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. 20. The value of 3 52 ( cos tan 1)x x x x dx π − π + + +∫ is (A) 0 (B) 2 (C) π (D) 1 21. The value of 2 4 3 sinlog 4 3 cos x dxx π + + ∫ is (A) 2 (B) 3 / 4 (C) 0 (D) -2