Calculus/Integration/Solutions

Integration of PolynomialsEdit

Evaluate the following:

1.  
 
 
2.  
 
 
3.  
 
 
4.  
 
 
5.  
 
 

Indefinite IntegrationEdit

Find the general antiderivative of the following:

6.  
 
 
7.  
 
 
8.  
 
 
9.  
 
 
10.  
 
 
11.  
 
 
12.  
 
 
13.  
Let
 

Then

 
Let
 

Then

 

Integration by partsEdit

14. Consider the integral  . Find the integral in two different ways. (a) Integrate by parts with   and  . (b) Integrate by parts with   and  . Compare your answers. Are they the same?
(a)
 
 
 

(b)

 
 
 

Notice that the answers in parts (a) and (b) are not equal. However, since indefinite integrals include a constant term, we expect that the answers we found will differ by a constant. Indeed

 
(a)
 
 
 

(b)

 
 
 

Notice that the answers in parts (a) and (b) are not equal. However, since indefinite integrals include a constant term, we expect that the answers we found will differ by a constant. Indeed