Section 13.3 Exercise Solutions

1. 1/6
 

2. 1/3
 

3. 
 

4. -13/6
 

5. (1 - cos 1)/2
 

6. 5/2 - 4 ln 2
 

7.  = 1/12
 

9.  = -19/42
 

11.  = (e4 - 4e)/2
 

13.  = (1 - cos 1)/2
 

15.  = 500/3
 

17.  = 1/8
 

19.  = 6/35
 

21.  = 31/8
 

23. 
 

25.  = 1/6
 

39.  = (e9 - 1)/6
 

41.  = (sin 81)/ 4
 

43.  [After the first integration there's a clever u = cos x substitution to be made]
 

47. Since for points in [0,1]  [0,1] the integrand is between 0 and , the value of the integral also lies between 0 and .