integral from 0 to 1 of 2pix\sqrt[3]{x}

Lösung

\int_{0}^{1} 2 π x 3 x d x

\frac{6 π}{7}

Dezimale

2.69279 \dots

Schritte zur Lösung

\int_{0}^{1} 2 π x 3 x d x

Entferne die Konstante:

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

= 2 π \cdot \int_{0}^{1} x 3 x d x

Wende die partielle Integration an

= 2 π [\frac{1}{2} x^{2} 3 x - \int \frac{1}{6} x^{\frac{4}{3}} d x]_{0}^{1}

\int \frac{1}{6} x^{\frac{4}{3}} d x = \frac{1}{14} x^{\frac{7}{3}}

= 2 π [\frac{1}{2} x^{2} 3 x - \frac{1}{14} x^{\frac{7}{3}}]_{0}^{1}

Vereinfache

2 π [\frac{1}{2} x^{2} 3 x - \frac{1}{14} x^{\frac{7}{3}}]_{0}^{1} : 2 π [\frac{3}{7} x^{2} 3 x]_{0}^{1}

= 2 π [\frac{3}{7} x^{2} 3 x]_{0}^{1}

Berechne die Grenzen:

\frac{3}{7}

= 2 π \frac{3}{7}

Vereinfache

= \frac{6 π}{7}

\frac{d}{d x} (8 x^{5} 2 π)

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

\frac{d}{d x} (\frac{x ^{2} + 6}{( 2 x - 7 ) ^{7}})

x \to 0 lim (\frac{200 π}{x})

n or ma l y = \frac{y + 5 x}{3 y - x}, (1, 2)