integral from-6 to 6 of (t^3-36t)(-20t)

Lösung

\int_{- 6}^{6} (t^{3} - 36 t) (- 20 t) d t

41472

Schritte zur Lösung

\int_{- 6}^{6} (t^{3} - 36 t) (- 20 t) d t

Vereinfache

= \int_{- 6}^{6} - 20 t (t^{3} - 36 t) d t

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - 20 \cdot \int_{- 6}^{6} t (t^{3} - 36 t) d t

Multipliziere aus

t (t^{3} - 36 t) : t^{4} - 36 t^{2}

= - 20 \cdot \int_{- 6}^{6} t^{4} - 36 t^{2} d t

Wende die Summenregel an:

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

= - 20 (\int_{- 6}^{6} t^{4} d t - \int_{- 6}^{6} 36 t^{2} d t)

\int_{- 6}^{6} t^{4} d t = \frac{15552}{5}

\int_{- 6}^{6} 36 t^{2} d t = 5184

= - 20 (\frac{15552}{5} - 5184)

Vereinfache

- 20 (\frac{15552}{5} - 5184) : 41472

= 41472

\int_{0}^{2 π} θ^{2} + 1 d θ

\int_{3}^{9} - x + 11 d x

\int_{0}^{x} \frac{1}{2} e^{- \frac{x}{2}} d x

\int_{0}^{c o s (θ)} sec^{2} (y) d y

\int_{0}^{4} 3 x - 8 d x