Problem Set (Evaluating Definite Integrals)
For questions 1-9, evaluate the definite integrals:

(  
Ans: 130

( ˆ  ‰
Ans:  
( Œ
Ans: 0.5

1.


2


3.


 •

( a  sin b



4.
Ans:   

5.
(


csc ab
Ans: 1/4

( a  b 

6.
Ans: 3/55

( È   

7.
 use 2 decimal places
Ans: 14.36

8.


( È
  

9.



(  ˆ  5‰ 

Ans: 8

Ans: 620.133

10.
A car's speed is given by        where     
where  is hours and  is miles/hour.
a) How far does the car travel in the 5 hours?
Ans: 166.7 miles
b) What is the average speed of the car?
Ans: 33.3 mph
Some Detailed Solutions
3.
I will use the property that '  ab   '  ab









( Œ 
( ˆ  ‰ 
•








     •   • 







   Œ  •           



5.
To evaluate (


csc ab, let        
   

  
csc ab  (
csc ab
 (
csc ab 
(

 






cotab
cotab
 


•
•






cota  b cota  b




cotab  cotab



 



To evaluate ( a  b , let         

6.

  

 

Then ( a  b  
  
  
(
 



 



 
 
• 
• 
 

   
   









 



8.
To evaluate (


, let         
 È  

    




 
  (
  (
  
( È


  

 



   È  •  ŠÈ  È‹ 


 a  b   

To evaluate (  ˆ  5‰  let          

9.

(    5‰  


ˆ 




(


  
  
     (
 


 
 
 
ˆ  ‰ • 
ˆ   ‰   


 




a) The distance traveled is ( ˆ    ‰ 

10.


     • 
      miles



 miles
b) Average speed is equal to


 
5 hours

 miles per hour.