integral from a to b of 2x

Lösung

\int_{a}^{b} 2 x d x

b^{2} - a^{2}

Schritte zur Lösung

\int_{a}^{b} 2 x d x

Entferne die Konstante:

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

= 2 \cdot \int_{a}^{b} x d x

Wende die Potenzregel an

= 2 [\frac{x ^{2}}{2}]_{a}^{b}

Berechne die Grenzen:

\frac{b ^{2}}{2} - \frac{a ^{2}}{2}

= 2 (\frac{b ^{2}}{2} - \frac{a ^{2}}{2})

Vereinfache

= b^{2} - a^{2}

\int_{\frac{π}{6}}^{\frac{π}{2}} sin (x) d x

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\int_{3}^{4} x^{2} - 9 d x