For this problem were given to functions. Y goes The absolute value of X shown here in blue and y equals X squared minus two shown here and cream were asked to identify the region between the curves, which I've done here in red, and to calculate the area. You can calculate the area in two ways you can do it is to separate inter girls, one going from negative to 01 from one. Going from X equals ear toe X equals two or you can do it is two times the area in one of those haves, since the area could be split into two equal hats. So the way I've done it is I did two times the integral from 0 to 2, so X equals zero X equals two of the function on top, minus the function on the bottom, which would be X since from 0 to 2, it's a pause. It's a slope with a It's a line with a slope of one so B y equals X minus the function on the bottom, which is X squared by this to so the area will be represented as two times the integral from 0 to 2 of X minus X squared, minus two DX Distributing the negative, we get two times the integral from 0 to 2 of X minus X squared plus two DX taking the integral of X. We add one to the exponents and then divide by the new exponents, so become 1/2 X squared and then x squared. We add one to the exponents divide by the new exponents, so becomes minus 1/3 x cubed. And then the constant simply gets a variable next to it. So plus two acts, we then plug in to for X. So it becomes to minus 8/3 plus four minus. And then we plug zero and fax, So just be minus zero, adding these together and then multiplying by two, you get the area to be 20/3.