integral from x to 2 of (xy)/2

Lösung

\int_{x}^{2} \frac{x y}{2} d y

\frac{x ( 4 - x ^{2} )}{4}

Schritte zur Lösung

\int_{x}^{2} \frac{x y}{2} d y

Entferne die Konstante:

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

= \frac{x}{2} \cdot \int_{x}^{2} y d y

Wende die Potenzregel an

= \frac{x}{2} [\frac{y ^{2}}{2}]_{x}^{2}

Berechne die Grenzen:

2 - \frac{x ^{2}}{2}

= \frac{x}{2} (2 - \frac{x ^{2}}{2})

Vereinfache

= \frac{x ( 4 - x ^{2} )}{4}

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

\int_{2}^{4} (25 - x^{2})^{2} d x

\int_{2}^{3} t 1 + 4 t^{2} d t

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\int_{2}^{5} 6 x - 12 d x