integral from 1 to 6 of t^2-2t-8

Lösung

\int_{1}^{6} t^{2} - 2 t - 8 d t

- \frac{10}{3}

Dezimale

- 3.33333 \dots

Schritte zur Lösung

\int_{1}^{6} t^{2} - 2 t - 8 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

= \int_{1}^{6} t^{2} d t - \int_{1}^{6} 2 t d t - \int_{1}^{6} 8 d t

\int_{1}^{6} t^{2} d t = \frac{215}{3}

\int_{1}^{6} 2 t d t = 35

\int_{1}^{6} 8 d t = 40

= \frac{215}{3} - 35 - 40

Vereinfache

\frac{215}{3} - 35 - 40 : - \frac{10}{3}

= - \frac{10}{3}

\int_{1}^{- 1} x^{2} d x

\int_{x^{2}}^{x} (x^{2} + y^{2}) d y

\int_{- 1}^{1} x^{7} d x

\int_{0}^{1} x (x^{2} + 6) d x

\int_{- 1}^{3} (3 x - 8) (x + 3) d x