integral from 0 to 4 of (2x^2+sqrt(x))

Lösung

\int_{0}^{4} (2 x^{2} + x) d x

48

Schritte zur Lösung

\int_{0}^{4} 2 x^{2} + x 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_{0}^{4} 2 x^{2} d x + \int_{0}^{4} x d x

\int_{0}^{4} 2 x^{2} d x = \frac{128}{3}

\int_{0}^{4} x d x = \frac{16}{3}

= \frac{128}{3} + \frac{16}{3}

Vereinfache

\frac{128}{3} + \frac{16}{3} : 48

= 48

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