# Calculus

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Find the area between the two curves y1= x^2 - 4x + 5 and y2 = 2x - 3, finding the points of intersection algebraically.

• Calculus -

intersection points:
x^2 - 4x + 5 = 2x-3
x^2 - 6x + 8 = 0
(x-2)(x-4) = 0
x = 2 or x = 4

in that domain, the effective height of the region is
2x-3 - (x^2-4x+5) = -x^2 + 6x - 8

area of region
= ∫(-x^2 + 6x - 8) dx from x = 2 to x = 4
= [ -x^3/3 + 3x^2 - 8x] from 2 to 3
= -9 + 27 - 24 - (-8/3 + 12 - 16)
= 2/3

check my arithmetic

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