integral from 0 to 5 of 2e^{0.2t}-t

Lösung

\int_{0}^{5} 2 e^{0.2 t} - t d t

10 e - \frac{45}{2}

Dezimale

4.68281 \dots

Schritte zur Lösung

\int_{0}^{5} 2 e^{0.2 t} - t 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} 2 e^{0.2 t} d t - \int_{0}^{5} t d t

\int_{0}^{5} 2 e^{0.2 t} d t = 10 (e - 1)

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

= 10 (e - 1) - \frac{25}{2}

Vereinfache

10 (e - 1) - \frac{25}{2} : 10 e - \frac{45}{2}

= 10 e - \frac{45}{2}

\int_{1}^{2} (3 x^{5} - 2 x^{3}) d x

\int_{0}^{t} e^{a t} d t

\int_{- 1}^{5} 2 x + 6 d x

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

\int_{- π}^{0} 6 x^{3} d x