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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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