integral from-1 to 4 of xsqrt(x+5)

Lösung

\int_{- 1}^{4} x x + 5 d x

\frac{316}{15}

Dezimale

21.06666 \dots

Schritte zur Lösung

\int_{- 1}^{4} x x + 5 d x

Wende U-Substitution an

= \int_{4}^{9} (u - 5) u d u

Multipliziere aus

(u - 5) u : u^{\frac{3}{2}} - 5 u

= \int_{4}^{9} u^{\frac{3}{2}} - 5 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_{4}^{9} u^{\frac{3}{2}} d u - \int_{4}^{9} 5 u d u

\int_{4}^{9} u^{\frac{3}{2}} d u = \frac{422}{5}

\int_{4}^{9} 5 u d u = \frac{190}{3}

= \frac{422}{5} - \frac{190}{3}

Vereinfache

\frac{422}{5} - \frac{190}{3} : \frac{316}{15}

= \frac{316}{15}

\int_{- 2}^{1} \frac{3}{4 + x} d x

\int_{2}^{4} sin (x) d x

\int_{- 4}^{4} (- 3 x^{4} + 1) d x

\int_{3}^{9} e^{x} d x

\int_{1}^{2} 1.5 x d x