integral from b to a of f(x)

Lösung

\int_{b}^{a} f (x) d x

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Potenzregel an

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

Berechne die Grenzen:

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

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

Vereinfache

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

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

x \to 0 lim (e^{x^{2}})

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

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\int_{0}^{\frac{π}{3}} (sec^{2} (x)) d x