integral from 0 to 1 of 10^{3x}+10^{-3x}

Lösung

\int_{0}^{1} 1 0^{3 x} + 1 0^{- 3 x} d x

\frac{333333}{1000 ln ( 10 )}

Dezimale

144.76468 \dots

Schritte zur Lösung

\int_{0}^{1} 1 0^{3 x} + 1 0^{- 3 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} 1 0^{3 x} d x + \int_{0}^{1} 1 0^{- 3 x} d x

\int_{0}^{1} 1 0^{3 x} d x = \frac{333}{ln ( 10 )}

\int_{0}^{1} 1 0^{- 3 x} d x = \frac{333}{1000 ln ( 10 )}

= \frac{333}{ln ( 10 )} + \frac{333}{1000 ln ( 10 )}

Vereinfache

\frac{333}{ln ( 10 )} + \frac{333}{1000 ln ( 10 )} : \frac{333333}{1000 ln ( 10 )}

= \frac{333333}{1000 ln ( 10 )}

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