Calculus

Calculate the area of the region bounded by the graphs of the given equations

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

The answer is supposed to be 9/8, but I'm getting -111/8. Idk what I'm doing wrong

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  1. graph them
    first zeros
    (x-4)(x-1) = 0
    x = 1 and x = 4
    and
    x = 1 and x = 1 (vertex on x axis, in lower quadrants(sheds water)
    SO
    We are looking only at some region between x = 1(where they intersect, and somewhere between x = 1 and x = 4 where they hit again
    Where is that?
    x^2 -5 x +4 = -(x^2-2x+1) =-x^2+2x -1
    2 x^2 - 7 x + 5 = 0
    x = [ 7 +/- sqrt (49-40)]/4
    x = [ 7+/- 3 ]/4
    x = 1 (we know that already)
    and x = 10/4 = 5/2 = 2.5
    which is about what we thought
    SO
    do your area between x = 1 and x = 2.5 :)

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  2. too bad you can't be bothered to show us your work ...

    The curves intersect at (1,0) and (5/2,-9/4). A quick look at the graphs shows that vertical strips will be easiest to work with, so the area is

    ∫[1,5/2] (-(x-1)^2)-(x^2-5x+4) dx
    = ∫[1,5/2] -2x^2+7x-5 dx
    = -2/3 x^3 + 7/2 x^2 - 5x [1,5/2]
    = (-25/24) - (-13/6)
    = 27/24
    = 9/8

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