MA1014_HW7r_201012

MA1014_HW7r_201012 - Mathematics
for
Engineering
II


Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Mathematics
for
Engineering
II
 Homework
7:
Integration
using
trigonometric
identities
 Function 5. ∫ cos5 x sin 4 xdx 6. € € ∫ sin (mx )dx π /4 0 π /2 3 13. 14. ∫ sin 0 4 x cos 2 xdx x cos 2 xdx x cos x dx x tan 3 xdx x sin 2 xdx xdx tdt 5 € € Result 1 2 1 = sin 5 x − sin 7 x + sin 9 x + C 5 7 9 1 1 = cos 3 mx − cos mx + C 3m m π 4 1 1 13 1 x − 4 sin( 4 x ) − 3 sin (2 x ) = 192 ( 3π − 4 ) 0 16 2 π 1 1 x − sin( 4 x ) = 0 8 4 16 2 2 = cos 3 x − cos x cos x + C 7 3 1 = cos2 x − ln cos x + C 2 1 = − cos4 x + C 2 = tan x − x + C 1 2 = tan 5 t + tan 3 t + tan t + C 5 3 1 1 = sec 7 (2 x ) − sec 5 (2 x ) + C 14 10 16 14 = tan θ + tan θ + C 6 4 = ln csc x − cot x + C ó = − ln csc x + cot x + C 1 = (ln csc x − cot x + ln sec x + tan x ) + C ó 2 1 = − (ln csc x + cot x + ln sec x + tan x ) + C 2 1 = sin 2 x + C 2 1 = tan 5 ( t 2 ) + C 10 π ∫ sin ∫ sin ∫ cos ∫ cos ∫ tan ∫ sec 2 € € € € € € € € 15. 17. 20. 23. 25. 28. 33. 39. 44. 3 € € € € € € € € € 2 2 2 6 ∫ tan (2 x ) sec (2 x )dx 3 ∫ cos θ dθ ∫ csc xdx 4 tan 3 θ € € ∫ cos x + sin x dx sin 2 x € € € € € € € 1 − tan 2 x dx 45. ∫ sec 2 x 47. ∫ t sec 2 ( t 2 ) tan 4 ( t 2 )dt 
 € € fpm@itesm.mx

 ...
View Full Document

This note was uploaded on 12/26/2010 for the course MT 1014 taught by Professor Franciscoperez during the Fall '10 term at ITESM.

Ask a homework question - tutors are online