April 28th, 2012, 06:01 AM  #1 
Member Joined: Mar 2012 Posts: 52 Thanks: 0  Find the area
1 Find the area of the region bounded by y=x^33x^2+2x , the xaxis, x = 0, and x = 2. 
April 28th, 2012, 06:40 AM  #2 
Newbie Joined: Apr 2012 Posts: 11 Thanks: 0  Re: Find the area
Calculate the integral from x= 0 to x=2 and you'll get that the integral equals 0.

April 28th, 2012, 07:01 AM  #3 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Find the area
Since the area is being asked for, you need to compute: You need to find the roots of the integrand and determine on which intervals it is positive and on which it is negative. positive negative Hence: With a translation of axes, replacing x with x + 1, we find the integrand is odd about the line x = 1, and we may use this symmetry to write: 
April 28th, 2012, 09:22 AM  #4 
Member Joined: Mar 2012 Posts: 52 Thanks: 0  Re: Find the area
Thanks! The Area= 1/2 U^2


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