integral from 20 to 30 of k(x^2+y^2)

Lösung

\int_{20}^{30} k (x^{2} + y^{2}) d y

k (10 x^{2} + \frac{19000}{3})

Schritte zur Lösung

\int_{20}^{30} k (x^{2} + y^{2}) d y

Entferne die Konstante:

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

= k \cdot \int_{20}^{30} x^{2} + y^{2} d y

Wende die Summenregel an:

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

= k (\int_{20}^{30} x^{2} d y + \int_{20}^{30} y^{2} d y)

\int_{20}^{30} x^{2} d y = 10 x^{2}

\int_{20}^{30} y^{2} d y = \frac{19000}{3}

= k (10 x^{2} + \frac{19000}{3})

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

\int_{0}^{1} 6 x - x^{2} d x

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

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