integral from 1 to 5 of t^2-2t-15

Lösung

\int_{1}^{5} t^{2} - 2 t - 15 d t

- \frac{128}{3}

Dezimale

- 42.66666 \dots

Schritte zur Lösung

\int_{1}^{5} t^{2} - 2 t - 15 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}^{5} t^{2} d t - \int_{1}^{5} 2 t d t - \int_{1}^{5} 15 d t

\int_{1}^{5} t^{2} d t = \frac{124}{3}

\int_{1}^{5} 2 t d t = 24

\int_{1}^{5} 15 d t = 60

= \frac{124}{3} - 24 - 60

Vereinfache

\frac{124}{3} - 24 - 60 : - \frac{128}{3}

= - \frac{128}{3}

\int_{- 1}^{8} (10 x - x^{2}) - (3 x - 8) d x

\int_{4}^{7} \frac{x}{x - 3} d x

\int_{0}^{8} 11000 e^{- 0.019 t} d t

\int_{0}^{3} (5 x - 9) d x

\int_{0}^{4} 1 + x^{\frac{1}{2}} d x