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December 22, 2014

December 22, 2014

Posted by **tiffany** on Wednesday, December 11, 2013 at 6:34pm.

Enclosed by y = x^2 − 4x + 1 and y = −x^2 + 4x − 5

- Calculus -
**Reiny**, Wednesday, December 11, 2013 at 6:57pmHere is a sketch

http://www.wolframalpha.com/input/?i=plot+y+%3D+x%5E2+−+4x+%2B+1+and+y+%3D+−x%5E2+%2B+4x+−+5

Easy to find their intersection points:

(1, -2) and (3, -2)

effective height between x = 1 and x = 3

= (-x^2 + 4x - 5) - (x^2 - 4x + 1)

= -2x^2 +8x -6

area = ∫(-2x^2 + 8x - 6) dx from x = 1 to 3

= [(-2/3)x^3 + 4x^2 - 6x] from 1 to 3

= ( -18 + 36 - 18) - (-2/3 + 4 - 6)

= 8/3

check my arithmetic

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