integral from 2 to 6 of 3pi(sqrt(x^5))

Lösung

\int_{2}^{6} 3 π (x^{5}) d x

\frac{3 π ( 432 6 - 16 2 )}{7}

Dezimale

1394.26415 \dots

Schritte zur Lösung

\int_{2}^{6} 3 π x^{5} d x

Entferne die Konstante:

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

= 3 π \cdot \int_{2}^{6} x^{5} d x

x^{5} = x^{\frac{5}{2}},

angenommen

x \geq 0

= 3 π \cdot \int_{2}^{6} x^{\frac{5}{2}} d x

Wende die Potenzregel an

= 3 π [\frac{2}{7} x^{\frac{7}{2}}]_{2}^{6}

Berechne die Grenzen:

\frac{432 6 - 16 2}{7}

= 3 π \frac{432 6 - 16 2}{7}

Vereinfache

= \frac{3 π ( 432 6 - 16 2 )}{7}

\int_{0}^{2} x^{3} e^{- x^{4}} d x

\int_{0}^{2} x^{3} (4 + x^{4})^{3} d x

\int_{0}^{5} (x^{3}) d x

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

\int_{0}^{π} - x cos (x) + x d x