integral from y^2 to y of (x^n+y^n)

Lösung

\int_{y^{2}}^{y} (x^{n} + y^{n}) d x

y^{n + 1} - y^{n + 2} + \frac{y ^{n + 1} - y ^{2 (n + 1)}}{n + 1}

Schritte zur Lösung

\int_{y^{2}}^{y} x^{n} + y^{n} d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{y^{2}}^{y} y^{n} d x + \int_{y^{2}}^{y} x^{n} d x

\int_{y^{2}}^{y} y^{n} d x = y^{n + 1} - y^{n + 2}

\int_{y^{2}}^{y} x^{n} d x = \frac{y ^{n + 1} - y ^{2 (n + 1)}}{n + 1}

= y^{n + 1} - y^{n + 2} + \frac{y ^{n + 1} - y ^{2 (n + 1)}}{n + 1}

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