integral from 0 to 2 of 1/((2-x)^{4/5)}

Lösung

\int_{0}^{2} \frac{1}{( 2 - x ) ^{\frac{4}{5}}} d x

5 \cdot 2^{\frac{1}{5}}

Dezimale

5.74349 \dots

Schritte zur Lösung

\int_{0}^{2} \frac{1}{( 2 - x ) ^{\frac{4}{5}}} d x

Wende U-Substitution an

= \int_{2}^{0} - \frac{1}{u ^{\frac{4}{5}}} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{0}^{2} - \frac{1}{u ^{\frac{4}{5}}} d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - (- \int_{0}^{2} \frac{1}{u ^{\frac{4}{5}}} d u)

Wende die Potenzregel an

= - (- [5 u^{\frac{1}{5}}]_{0}^{2})

Vereinfache

= [5 u^{\frac{1}{5}}]_{0}^{2}

Berechne die Grenzen:

5 \cdot 2^{\frac{1}{5}}

= 5 \cdot 2^{\frac{1}{5}}

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

\int_{0}^{2 x} sin (t^{2}) d t

\int_{0}^{x} y e^{- y x} d x

\int_{\frac{1}{2}}^{2} \frac{1}{x ( x + 1 )} d x

\int_{0}^{5} (x - 5) (x - 3) d x