integral from 0 to 4 of (sqrt(x+3x))

Lösung

\int_{0}^{4} (x + 3 x) d x

\frac{32}{3}

Dezimale

10.66666 \dots

Schritte zur Lösung

\int_{0}^{4} x + 3 x d x

Vereinfache

x + 3 x : 2 x

= \int_{0}^{4} 2 x d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int_{0}^{4} x d x

Wende die Potenzregel an

= 2 [\frac{2}{3} x^{\frac{3}{2}}]_{0}^{4}

Berechne die Grenzen:

\frac{16}{3}

= 2 \cdot \frac{16}{3}

Vereinfache

= \frac{32}{3}

\int_{0}^{\frac{π}{2}} 6 sin (\frac{x}{2}) d x

\int_{0}^{3} (3 x^{2} - 6) d x

\int_{0}^{1} 9 t^{4} + 16 t^{2} d t

\int_{0}^{2} \frac{x ^{3}}{4} d x

\int_{0}^{x} \frac{1}{1 - x ^{2}} d x