integral from 0 to 1 of (5^x-2^x)

Lösung

\int_{0}^{1} (5^{x} - 2^{x}) d x

\frac{4}{ln ( 5 )} - \frac{1}{ln ( 2 )}

Dezimale

1.04264 \dots

Schritte zur Lösung

\int_{0}^{1} 5^{x} - 2^{x} 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}^{1} 5^{x} d x - \int_{0}^{1} 2^{x} d x

\int_{0}^{1} 5^{x} d x = \frac{4}{ln ( 5 )}

\int_{0}^{1} 2^{x} d x = \frac{1}{ln ( 2 )}

= \frac{4}{ln ( 5 )} - \frac{1}{ln ( 2 )}

\int_{0}^{3} 2 x (x - 6) d x

\int_{- 1}^{0} 2 x^{2} (4 x^{3} - 1)^{3} d x

\int_{0}^{2} 2 x e^{x} - e^{x} + e^{- x} d x

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

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