what is the area of region between the curves y=x^2+6 and y=(x-3)^2+4x-7?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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To find the area between the curves, we first need to determine their points of intersection.

y = x^2 + 6 and y = (x-3)^2 + 4x - 7

Equate the two

x^2 + 6 = (x - 3)^2 + 4x - 7

=> x^2 + 6 = x^2 + 9 - 6x + 4x - 7

=> 4 = -2x

=> x = -2

y = 10

We see that the two curves intersect at only one point. Therefore we cannot find the area of the region enclosed between them.

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