integral from 7 to 10 of xsqrt(x-6)

Lösung

\int_{7}^{10} x x - 6 d x

\frac{202}{5}

Dezimale

40.4

Schritte zur Lösung

\int_{7}^{10} x x - 6 d x

Wende U-Substitution an

= \int_{1}^{4} (u + 6) u d u

Multipliziere aus

(u + 6) u : u^{\frac{3}{2}} + 6 u

= \int_{1}^{4} u^{\frac{3}{2}} + 6 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_{1}^{4} u^{\frac{3}{2}} d u + \int_{1}^{4} 6 u d u

\int_{1}^{4} u^{\frac{3}{2}} d u = \frac{62}{5}

\int_{1}^{4} 6 u d u = 28

= \frac{62}{5} + 28

Vereinfache

\frac{62}{5} + 28 : \frac{202}{5}

= \frac{202}{5}