integral from 1 to 3 of x^2*f(x^3)

Lösung

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

\frac{364 f}{3}

Schritte zur Lösung

\int_{1}^{3} x^{2} f x^{3} d x

Entferne die Konstante:

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

= f \cdot \int_{1}^{3} x^{2} x^{3} d x

Vereinfache

x^{2} x^{3} : x^{5}

= f \cdot \int_{1}^{3} x^{5} d x

Wende die Potenzregel an

= f [\frac{x ^{6}}{6}]_{1}^{3}

Berechne die Grenzen:

\frac{364}{3}

= f \frac{364}{3}

Vereinfache

= \frac{364 f}{3}

\int_{0}^{2} (- x + 2) d x

\int_{0}^{2} \frac{x ^{2}}{x ^{3} + 7} d x

\int_{- 1}^{0} x ln (1 - x) d x

\int_{9}^{1} \frac{1}{x} d x

\int_{1}^{x} t^{2} - t d t