integral from 9 to 18 of xsqrt(x-9)

Lösung

\int_{9}^{18} x x - 9 d x

\frac{1296}{5}

Dezimale

259.2

Schritte zur Lösung

\int_{9}^{18} x x - 9 d x

Wende U-Substitution an

= \int_{0}^{9} (u + 9) u d u

Multipliziere aus

(u + 9) u : u^{\frac{3}{2}} + 9 u

= \int_{0}^{9} u^{\frac{3}{2}} + 9 u d u

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}^{9} u^{\frac{3}{2}} d u + \int_{0}^{9} 9 u d u

\int_{0}^{9} u^{\frac{3}{2}} d u = \frac{486}{5}

\int_{0}^{9} 9 u d u = 162

= \frac{486}{5} + 162

Vereinfache

\frac{486}{5} + 162 : \frac{1296}{5}

= \frac{1296}{5}

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