Question

HELP PLEASE??
set up the definite integral that gives the area
of the region.

Answer 1

assuming that that the curves/line are symmetrical about y=1... take the integral of f() and g() then subtract them and multiply by 2

Answer 2

@lxry0h i dont know how to set up the integral

Answer 3

hold up I give you a proper equation

Answer 4

\[2[\int\limits_{}^{}(x-1)^{3}dx-\int\limits_{}^{}(x-1)dx]\]

Answer 5

well... oops I forgot the limits of integration

Answer 6

\[2*[\int\limits_{1}^{2}(x-1)^{3} dx-\int\limits_{1}^{2}(x-1)dx]\]

Answer 7

\[simply just find \it \int\limits_{-1}^{1}[f(x)-g(x)]+\int\limits_{1}^{2}[f(x)-g(x)]\]

Answer 8

if you want some intuition about the problem, think of it this way. taking the integral of g(x) from 1 to 2 will give you the entire area under g(x) from x=1 -to x=2. but you you don't want the whole thing do you? no. if you take the area under f(x) as well from 1 to 2 you can obtain the area of JUST the place under it. now to set this up algebraically:
let the entire area under g(x) be A;
let the area under f(x) be B;
and let the area that's shaded in the picture be C;
you know that B+C = A. right? so A-B=C

Answer 9

@lxry0h okay thank you (: