Definite Integrals - Random Signals and Processes Primer with MATLAB - page 505

Appendix A: Definite Integrals

1. 1
0

x n e ax d x ¼ G ð n þ 1 Þ
a nþ 1

a > 0 ; n > 1

;

1

cos ax
1 þ x 2 d x ¼

p
2 e jaj

2.

0

p

1

p

e b 2 e a 2 x 2 cos bx d x ¼ 3. a > 0

;

4 a 2

2 a

0

(

2
2 a nþ 1 2 ¼

1 3 ð 2 k 1 Þ

1

p

nþ 1

x n e ax 2 d x ¼ G

n ¼ 2 k

4.

n ¼ 2 k þ 1 ;

k ¼ 0 ; 1 ; 2 ; ...

2 kþ 1 a kþ 1 = 2

k !
2 a kþ 1

0

ð

p

b 2
4 ;

1
2 p

e jb sin x d x 1

5. I 0 ðbÞ¼ for b << 1

p

1 p

p

e a 2 x 2 þbx d x ¼ e b 2

= 4 a 2

6. ; a > 0

a

1

1

a p

2 ;

7.

þ x 2 d x ¼

a > 0

a 2

0

1

sin 2 ax
x 2 d x ¼jajp= 2 ;

a > 0

8.

0