Integral of a Polynomial

Date: 7/15/96 at 8:50:45
From: COMPAQ PRESARIO 9240
Subject: Integral of a Polynomial

Find the integral of (5x-1) to the power of 6. I just forgot how to do 
it!

Date: 7/15/96 at 9:50:17
From: Doctor Paul
Subject: Re: Integral of a Polynomial

You want this I believe:
                                 /
                                |           6
                                |  (5 x - 1)  dx
                                |
                               /

Let's recall the rule for integrating polynomials.  Add one to the 
exponent, divide by the new exponent, and then divide by the 
derivitive of the integrand.  Don't forget the constant of 
integration. Here we go:

                                            7
                       (1/7)*(1/5)*(5 x - 1)  + C

and that simplifies to:

                                            7
                              1/35 (5 x - 1)  + C

The good thing about integration is that we can check our answer and 
make sure that the derivative of our answer is what we started with.  
Let's do that:

             6
7/35 (5 x -1) (5)

that simplifies to:
     
             6
     (5 x -1)

And that's what you started with so we know our answer is right.

-Doctor Paul,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/