integral from-3 to 0 of xsqrt(x+3)

Lösung

\int_{- 3}^{0} x x + 3 d x

\frac{18 3}{5} - 63

Dezimale

- 4.15692 \dots

Schritte zur Lösung

\int_{- 3}^{0} x x + 3 d x

Wende U-Substitution an

= \int_{0}^{3} (u - 3) u d u

Multipliziere aus

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

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

\int_{0}^{3} u^{\frac{3}{2}} d u = \frac{18 3}{5}

\int_{0}^{3} 3 u d u = 63

= \frac{18 3}{5} - 63

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