integral from 0 to 4 of (3sqrt(t)-2e^t)

Lösung

\int_{0}^{4} (3 t - 2 e^{t}) d t

- 2 e^{4} + 18

Dezimale

- 91.19630 \dots

Schritte zur Lösung

\int_{0}^{4} 3 t - 2 e^{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}^{4} 3 t d t - \int_{0}^{4} 2 e^{t} d t

\int_{0}^{4} 3 t d t = 16

\int_{0}^{4} 2 e^{t} d t = 2 (e^{4} - 1)

= 16 - 2 (e^{4} - 1)

Vereinfache

16 - 2 (e^{4} - 1) : - 2 e^{4} + 18

= - 2 e^{4} + 18

\int_{- 2}^{5} (x^{2} - 4) d x

\frac{d}{d x} ((5 x^{4} - 6 x^{3} + x)^{5})

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

\frac{d}{d s} (\frac{- s ^{2} + 1}{( s ^{2} + 1 ) ^{2}})

\frac{\partial}{\partial x} (x^{2 + 2 y^{2} + 3 z^{2}})