Question 6.8.P.1: Let q1(t) = 1, q2(t )= t , and q3(t ) = 3t ^2 - 4. Verify th...

Compute

\left\langle q_{1}, q_{2}\right\rangle=\int_{-2}^{2} 1 \cdot t d t=\left.\frac{1}{2} t^{2}\right|_{-2} ^{2}=0.

\left\langle q_{1}, q_{3}\right\rangle=\int_{-2}^{2} 1 \cdot\left(3 t^{2}-4\right) d t=\left.\left(t^{3}-4 t\right)\right|_{-2} ^{2}=0.

\left\langle q_{2}, q_{3}\right\rangle=\int_{-2}^{2} t \cdot\left(3 t^{2}-4\right) d t=\left.\left(\frac{3}{4} t^{4}-2 t^{2}\right)\right|_{-2} ^{2}=0.