integral from x to 2x of xy^3

Lösung

\int_{x}^{2 x} x y^{3} d y

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

Schritte zur Lösung

\int_{x}^{2 x} x y^{3} d y

Entferne die Konstante:

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

= x \cdot \int_{x}^{2 x} y^{3} d y

Wende die Potenzregel an

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

Berechne die Grenzen:

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

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

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