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April 28th, 2012, 06:01 AM   #1
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Find the area

1- Find the area of the region bounded by y=x^3-3x^2+2x , the x-axis, x = 0, and
x = 2.
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April 28th, 2012, 06:40 AM   #2
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Re: Find the area

Calculate the integral from x= 0 to x=2 and you'll get that the integral equals 0.
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April 28th, 2012, 07:01 AM   #3
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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:

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April 28th, 2012, 09:22 AM   #4
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Re: Find the area

Thanks! The Area= 1/2 U^2
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