integral from 0 to 2x^2 of 3xy

Lösung

\int_{0}^{2 x^{2}} 3 x y d y

6 x^{5}

Schritte zur Lösung

\int_{0}^{2 x^{2}} 3 x y d y

Entferne die Konstante:

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

= 3 x \cdot \int_{0}^{2 x^{2}} y d y

Wende die Potenzregel an

= 3 x [\frac{y ^{2}}{2}]_{0}^{2 x^{2}}

Berechne die Grenzen:

2 x^{4}

= 3 x \cdot 2 x^{4}

Vereinfache

= 6 x^{5}

\int_{- 1}^{2} x (x + 1) (x - 2) d x

\int_{0}^{3} (3 - x)^{\frac{- 1}{2}} d x

\int_{- 6}^{1} x^{3} d x

\int_{1}^{2} (e^{3 t} - \frac{4}{t}) d t

\int_{3}^{5} x e^{x^{2}} d x