Question

Find area bounded by f(x) =x^2 and g(x) =x+2

Answer 1

The sought area is painted red. We can find it using integration, so

$S=\int_{-1}^{2}(x+2-x^2)dx={\frac {x^2} 2}_{x=-1}^{x=2}+2x_{x=-1}^{x=2}-{\frac {x^3} 3}|_{x=-1}^{x=2}=2-{\frac 1 2}+4+2-{\frac 8 3}+{\frac 1 3}={\frac {31} 6}$