integral from y^2 to y of 2y

Lösung

\int_{y^{2}}^{y} 2 y d y

y^{2} - y^{4}

Schritte zur Lösung

\int_{y^{2}}^{y} 2 y d y

Entferne die Konstante:

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

= 2 \cdot \int_{y^{2}}^{y} y d y

Wende die Potenzregel an

= 2 [\frac{y ^{2}}{2}]_{y^{2}}^{y}

Berechne die Grenzen:

\frac{y ^{2}}{2} - \frac{y ^{4}}{2}

= 2 (\frac{y ^{2}}{2} - \frac{y ^{4}}{2})

Vereinfache

= y^{2} - y^{4}

\int_{1}^{3} 4 - (x - 3)^{2} d x

\int_{1}^{4} (a x + \frac{1}{x})^{2} d x

\int_{1}^{2} (\frac{x e ^{x}}{y}) d y

\int_{0}^{1} 2 t \cdot 1 + 4 t^{2} d t

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