integral from-2 to 2 of (3xy^2)/(x^2+1)

Lösung

\int_{- 2}^{2} \frac{3 x y ^{2}}{x ^{2} + 1} d y

\frac{16 x}{1 + x ^{2}}

Schritte zur Lösung

\int_{- 2}^{2} \frac{3 x y ^{2}}{x ^{2} + 1} d y

Entferne die Konstante:

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

= \frac{3 x}{1 + x ^{2}} \cdot \int_{- 2}^{2} y^{2} d y

Wende die Potenzregel an

= \frac{3 x}{1 + x ^{2}} [\frac{y ^{3}}{3}]_{- 2}^{2}

Berechne die Grenzen:

\frac{16}{3}

= \frac{3 x}{1 + x ^{2}} \cdot \frac{16}{3}

Vereinfache

= \frac{16 x}{1 + x ^{2}}

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