f ( x ) = x {\displaystyle f(x)=x}
( 0 , 0 ) {\displaystyle (0,0)} ( 1 , 1 ) {\displaystyle (1,1)}
g ( x ) = x 2 {\displaystyle g(x)=x^{2}}
∫ 0 1 ( R − r ) d x {\displaystyle \int _{0}^{1}\left(R-r\right)dx}
R = x {\displaystyle R=x}
r = x 2 {\displaystyle r=x^{2}}
∫ 0 1 ( x − x 2 ) d x {\displaystyle \int _{0}^{1}\left(x-x^{2}\right)dx}
x 2 2 − x 3 3 | 0 1 {\displaystyle {\frac {x^{2}}{2}}-{\frac {x^{3}}{3}}{\bigg |}_{0}^{1}}
= 1 2 2 − 1 3 3 − 0 2 2 − 0 3 3 {\displaystyle ={\frac {1^{2}}{2}}-{\frac {1^{3}}{3}}-{\frac {0^{2}}{2}}-{\frac {0^{3}}{3}}}
= 1 6 {\displaystyle ={\frac {1}{6}}}
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