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## Homework Statement

So i think i got this straight since my last question. let's see :)

So my area of integration is: y=4 ; y=x

^{2}and y=(x-2)

^{2}

the function is |x-1|

i must integrate with respect to dx first.

## The Attempt at a Solution

So i sketched the area (see attatchment graphs should be cross at x=1 sorry for my bad sketch xD) and found that the upper limit for dx is x

^{2}(so y

^{½}) and the lower is (x-2)(so y

^{½}-2)

^{2}

then noticed that since the function is the absolute value of x-1 i can divide it up into 2 functions

-x+1 (for x<1) and x-1 (for x>1) and with that in mind in my sketch i drew the line x=1 so my integrals are:

∫

_{y½-2}

^{1}(-x+1) dx (this integral is from y

^{½}-2 to 1)

and ∫

_{1}

^{y½}(x-1)dx (this integral is from 1 to y

^{½})

and then integrate all this with respect to y from 0 to 4.