6.1 Areas Between Curves/7

$f(x)=x$

$(0,0)$ $(1,1)$

$g(x)=x^{2}$

$\int _{0}^{1}\left(R-r\right)dx$

$R=x$

$r=x^{2}$

$\int _{0}^{1}\left(x-x^{2}\right)dx$

${\frac {x^{2}}{2}}-{\frac {x^{3}}{3}}{\bigg |}_{0}^{1}$

$={\frac {1^{2}}{2}}-{\frac {1^{3}}{3}}-{\frac {0^{2}}{2}}-{\frac {0^{3}}{3}}$

$={\frac {1}{6}}$

File:File:6.1 Graph Q1.png