find the area of the region enclosed by y= square root of x, y=x-2, and y=0.

Question

i use f(x) - g(x) and got the answer to be 2, but my classmate got 8/3 do i'm really confuse don't know whats the answer.

Answer 1

Since y = x-2 starts below the x axis, I don't know whether to treat the region between the negative part of the parabola y = sqrtx and y = x-2 as the enclosed area. You get a much larger enclosed area if you only use y = +sqrtx to define the enclosed area. The end of the enclosed area is then where
x - 2 = sqrt x
x^2 -4x + 4 = x
(x-4)(x-1) = 0
x = 4 is the upper limit of x-integration if you don't use the negative part of the y = sqrtx curve.