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}

t \to 0 lim (\frac{5}{t} - \frac{5}{e ^{t} - 1})

a re a y = x^{2} - 1, x = - 2, x = 1

\int 1 + (\frac{4}{3 x})^{2} d x

\frac{d}{d x} (3 (4 - 9 x)^{4})

\int \frac{7 e ^{7 x}}{1 + e ^{7 x}} d x