integral from x^2 to x of 4xy

Lösung

\int_{x^{2}}^{x} 4 x y d y

2 x (- x^{4} + x^{2})

Schritte zur Lösung

\int_{x^{2}}^{x} 4 x y d y

Entferne die Konstante:

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

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

Wende die Potenzregel an

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

Berechne die Grenzen:

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

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

Vereinfache

= 2 x (- x^{4} + x^{2})

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