## Elementary Linear Algebra 7th Edition

We have $$\langle x, x\rangle=\int_{-1}^1 x^2 d x=\left[ \frac{ 1}{3 } x^3\right]_{-1}^1=\frac{ 1}{3 }+\frac{ 1}{3 } =\frac{ 2}{3 }.$$