integral from 0 to 5 of t^2+2t-15

Lösung

\int_{0}^{5} t^{2} + 2 t - 15 d t

- \frac{25}{3}

Dezimale

- 8.33333 \dots

Schritte zur Lösung

\int_{0}^{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_{0}^{5} t^{2} d t + \int_{0}^{5} 2 t d t - \int_{0}^{5} 15 d t

\int_{0}^{5} t^{2} d t = \frac{125}{3}

\int_{0}^{5} 2 t d t = 25

\int_{0}^{5} 15 d t = 75

= \frac{125}{3} + 25 - 75

Vereinfache

\frac{125}{3} + 25 - 75 : - \frac{25}{3}

= - \frac{25}{3}

\int_{1}^{\infty} \frac{4}{x ^{4}} d x

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

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

\int_{0}^{1} \frac{6}{t ^{2} + 1} d t

\int_{0}^{8} 25 - 2 x d x