integral from 0 to 4 of 1/((4-x)^{3/2)}

Lösung

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

divergiert

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{4}^{0} - \frac{1}{u ^{\frac{3}{2}}} d u

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

= - \int_{0}^{4} - \frac{1}{u ^{\frac{3}{2}}} d u

Entferne die Konstante:

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

= - (- \int_{0}^{4} \frac{1}{u ^{\frac{3}{2}}} d u)

Wende die Potenzregel an

= - (- [- \frac{2}{u ^{\frac{1}{2}}}]_{0}^{4})

Vereinfache

= [- \frac{2}{u ^{\frac{1}{2}}}]_{0}^{4}

Berechne die Grenzen:

divergiert

= divergiert

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

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