integral from 0 to 4 of (e^{-0.25x}+5)

Lösung

\int_{0}^{4} (e^{- 0.25 x} + 5) d x

- \frac{4}{e} + 24

Dezimale

22.52848 \dots

Schritte zur Lösung

\int_{0}^{4} e^{- 0.25 x} + 5 d x

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} e^{- 0.25 x} d x + \int_{0}^{4} 5 d x

\int_{0}^{4} e^{- 0.25 x} d x = 4 (1 - \frac{1}{e})

\int_{0}^{4} 5 d x = 20

= 4 (1 - \frac{1}{e}) + 20

Vereinfache

4 (1 - \frac{1}{e}) + 20 : - \frac{4}{e} + 24

= - \frac{4}{e} + 24

in v erse l a pl a ce \frac{1}{( s ^{2} + 1 ) ( s ^{2} )}

x \to 0 + lim (arccot (x))

\int (2 x^{2} + 3 x - 3) (5 x + 3) d x

d er i v a t i v e f (x) = \frac{x ^{4}}{8} - 8 x

x \to \infty lim (5 + \frac{1}{x})