integral from 0 to 3 of (xsqrt(1+x))

Lösung

\int_{0}^{3} (x 1 + x) d x

\frac{116}{15}

Dezimale

7.73333 \dots

Schritte zur Lösung

\int_{0}^{3} x 1 + x d x

Wende U-Substitution an

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

Multipliziere aus

(u - 1) u : u^{\frac{3}{2}} - u

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

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

\int_{1}^{4} u d u = \frac{14}{3}

= \frac{62}{5} - \frac{14}{3}

Vereinfache

\frac{62}{5} - \frac{14}{3} : \frac{116}{15}

= \frac{116}{15}

\int_{0}^{r} b \cdot r^{3} + c \cdot r^{2} d r

\int_{0}^{2} \frac{π}{2} r d r

\int_{1}^{3} 2 x - x^{2} d x

\int_{0}^{0.5} 4 x d x

\int_{0}^{π} (\frac{sin ( x )}{x}) d x