Let
be given by f ( x ) = − x 2 + 1 {\displaystyle {}f(x)=-x^{2}+1} , and g ( x ) = x 2 + x + 3 {\displaystyle {}g(x)=x^{2}+x+3} . Compute ⟨ f , g ⟩ {\displaystyle {}\left\langle f,g\right\rangle } in the sense of example.
![{\displaystyle f,g\colon [0,1]\longrightarrow \mathbb {R} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/3f28d086e1d8d3aadcfa9dd3ce5c687a328537d7)
