8)

\int f (t) = 0, 4 t^{3} - 2 t d x =

0, 1 t^{4} - t^{2} + c

F (a) = 0, 1 a^{4} - a^{2} + c

F (3) = 0, 1 * 2^{4} + 4^{2} - c

3 = 0, 16 - 16 + c

3 + 0, 16 - 16 = c

- 13, 16 = c

F (a) = 0, 1 t^{4} - t^{2} - 13, 16

\int_{- 2}^{a} - 2 x + 12 d x = 39

[- x^{2} + 12 x]_{- 2}^{a} = 39

(- a^{2} + 12 a) - (- (- 2)^{2} + 12 * (- 2)) = 39

(- a^{2} - 12 a) + 28 = 39

\underset{p q : - \frac{p}{2} \pm \sqrt{{\frac{p}{2}}^{2} - q} = - \frac{- 12}{2} \pm \sqrt{{\frac{- 12}{2}}^{2}} = 6 \pm 6 = [0, 12]}{\underset{⏟}{(a^{2} - 12 a)}} - 28 = - 39

a = [0, 12]