integral from 4 to 9 of xsqrt(x-3)

Lösung

\int_{4}^{9} x x - 3 d x

\frac{72 6 - 2}{5} + 126 - 2

Dezimale

62.26652 \dots

Schritte zur Lösung

\int_{4}^{9} x x - 3 d x

Wende U-Substitution an

= \int_{1}^{6} (u + 3) u d u

Multipliziere aus

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

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

\int_{1}^{6} u^{\frac{3}{2}} d u = \frac{72 6 - 2}{5}

\int_{1}^{6} 3 u d u = 126 - 2

= \frac{72 6 - 2}{5} + 126 - 2