4 x + y 2 = 12 , x = y {\displaystyle 4x+y^{2}=12,x=y}
4 x 4 = − y 2 + 12 4 {\displaystyle {\frac {4x}{4}}={\frac {-y^{2}+12}{4}}}
x = − 1 4 y 2 + 3 {\displaystyle x=-{\frac {1}{4}}y^{2}+3}
∫ 0 3 ( − 1 4 y 2 − y + 3 ) − y {\displaystyle \int _{0}^{3}(-{\frac {1}{4}}y^{2}-y+3)-y}
∫ 0 3 − 1 4 y 2 − y + 3 {\displaystyle \int _{0}^{3}-{\frac {1}{4}}y^{2}-y+3}
1 4 y 3 3 − y 2 2 + 3 y {\displaystyle {\frac {{\frac {1}{4}}y^{3}}{3}}-{\frac {y^{2}}{2}}+3y}
− 1 12 y 3 − 1 2 y 2 + 3 y | 0 3 {\displaystyle -{\frac {1}{12}}y^{3}-{\frac {1}{2}}y^{2}+3y{\bigg |}_{0}^{3}}
− 1 12 ( 3 ) 3 − 1 2 ( 3 ) 2 + 3 ( 3 ) {\displaystyle -{\frac {1}{12}}(3)^{3}-{\frac {1}{2}}(3)^{2}+3(3)}
= 2.25 {\displaystyle =2.25}
