THE ANTI-POWER RULE
 (also called "POWER RULE for anti-derivatives")

Earlier we encountered the power rule used in finding derivatives:
FUNCTION FORMAT: If f (x) = xn , then f '(x) = nxn-1
OPERATOR FORMAT: d

dx		 xn = nxn-1

We now notice that we can translate the above rule for derivatives into the language of anti-derivatives, as stated below:

THE ANTI-POWER RULE
FUNCTION FORMAT: If f (x) = xn , then f (x ) dx =   1  
n+1		 xn+1 + C
OPERATOR FORMAT: xn dx =   1  
n+1		 xn+1 + C

We first encountered the table below as examples of the power rule for derivatives, and we then filled in the boxes of the right-most 2 columns. This earlier table is enhanced below to include exercizes solved using the power rule for anti-derivatives: the ANTI-POWER RULE. As we did earlier, the first 14 rows will be completed in class or in an on-line exercise, emphasizing the first column. The last 4 rows are left as problems on your take-home test. For several of these problems, rules for exponents will be helpful.

f (x) dx =
FUNCTION
f (x) =		 n = f '(x)
  x2    
  x3    
  x10    
  x    
  1    
   1 

x		    
   1 

x2		    
   1 

x10		    
     
     
  1


    
  ()2    
  x    
  x


    
  .    
 



   
     
     

   
This page last
updated 9 January 2012