integral from 0 to 1 of ((y^2)^{5/2})/5

Lösung

\int_{0}^{1} \frac{( y ^{2} ) ^{\frac{5}{2}}}{5} d y

\frac{1}{30}

Dezimale

0.03333 \dots

Schritte zur Lösung

\int_{0}^{1} \frac{( y ^{2} ) ^{\frac{5}{2}}}{5} d y

Entferne die Konstante:

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

= \frac{1}{5} \cdot \int_{0}^{1} (y^{2})^{\frac{5}{2}} d y

(y^{2})^{\frac{5}{2}} = y^{5},

angenommen

y \geq 0

= \frac{1}{5} \cdot \int_{0}^{1} y^{5} d y

Wende die Potenzregel an

= \frac{1}{5} [\frac{y ^{6}}{6}]_{0}^{1}

Berechne die Grenzen:

\frac{1}{6}

= \frac{1}{5} \cdot \frac{1}{6}

Vereinfache

= \frac{1}{30}

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

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\int_{0}^{0.75} 2 d y