8.4 • IMPROPER I NTEGRALS INVOLVING TRIGONOMETRIC F UNCTIONS 315-------~EXERCISES FOR SECTION 8.4
Use residues to find the Cauchy principal value of- Joo COS X dx
- oo x2 + 9 d J
oo sinx dx
an 2.- oo x + 9
- Joo XCOSX dx
- oo x2 + 9 d J
oo xsinx dx
an -oo x2 + 9.3. Joo xsinx dx.- oo (x2 + 4)2
4. Joo cos x dx.
-oo (x2 + 4)25
Joo cosx dx. -oo (x2 + 4) (x 2 + 9)"
(^6). J- oo oo (x2 + COSX 1) (x2 dx + 4)"
7. Joo cosx dx.
-oo x^2 -2x+ 5
S Joo COSX dx
- -^00 x^2 - 4x + 5 ·
g, Joo xsinx dx.
-oo x4 + 4
3. d
lO. Joo X Sill X X.
- oo x 4 + 4