integral from-2 to x of (4t^2-3t)

解

\int_{- 2}^{x} (4 t^{2} - 3 t) d t

\frac{4 ( x ^{3} + 8 )}{3} - 3 (\frac{x ^{2}}{2} - 2)

解答ステップ

\int_{- 2}^{x} 4 t^{2} - 3 t d t

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{- 2}^{x} 4 t^{2} d t - \int_{- 2}^{x} 3 t d t

\int_{- 2}^{x} 4 t^{2} d t = \frac{4 ( x ^{3} + 8 )}{3}

\int_{- 2}^{x} 3 t d t = 3 (\frac{x ^{2}}{2} - 2)

= \frac{4 ( x ^{3} + 8 )}{3} - 3 (\frac{x ^{2}}{2} - 2)