Posted by weloo_volley on Tuesday, May 8, 2012 at 6:11pm.
for their points of intersection...
2x^2 - 3x - 1 = x^2 + 7x + 20
x^2 - 10x - 21 = 0
x^2 - 10x + 25 = 21 + 25 , I completed the square
(x-5)^2 = 46
x-5 = ± √46
x = 5 ± √46
so x = 5+√46 and x = 5-√46
or appr. 11.8 and -1.8
so I will take any value of x between these two values, x = 0 seems like a good choice, and find their y values
if x=0, y1 = -1, and if x=0 , y2 = 20
so the parabola y2 = .... is greater for all values of x between the two values we found
So the height of the region is
x^2+7x+20-(2x^2-3x-1) = -x^2 + 10x + 21
Area = ∫(-x^2 + 10x + 21) dx from x = 5-√46 to 5+√46
= [(-1/3)x^3 + 5x^2 + 21x] from x = 5-√46 to 5+√46
= ...
I will let you do the button-pushing arithmetic
Obviously we cannot demonstrate Mathcad on this webpage.
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