wgiven the functions
[tex]y=x^3[/tex][tex]y=x[/tex]
the area of the curve is given by the integral
the limits are defined by
[tex]y1=y2[/tex][tex]x^3=x[/tex][tex]x^3-x=0[/tex][tex]x(x+1)(x-1)=0[/tex][tex]x=0;x=-1;x=1[/tex]
the defined integral for the ara is given by
[tex]A=-\int_{-1}^0x-x^3dx+\int_0^1x-x^3dx[/tex][tex]A=2\int_0^1x-x^3dx[/tex][tex]A=2\lbrack\frac{x^2}{2}-\frac{x^4}{4}\rbrack_0^1[/tex][tex]A=2\lbrack\frac{1^2}{2}-\frac{1^4}{4}\rbrack_^-2\lbrack\frac{0^2}{2}-\frac{0^4}{4}\rbrack[/tex][tex]A=2\lbrack\frac{1^2}{2}-\frac{1^4}{4}\rbrack_^[/tex][tex]A=2*\frac{1}{4}[/tex][tex]A=\frac{2}{4}=\frac{1}{2}[/tex]
A= 1/2= 0.5
