integral from-2 to 2 of x^2+ax^3+bx^4

Lösung

\int_{- 2}^{2} x^{2} + a x^{3} + b x^{4} d x

\frac{64 b}{5} + \frac{16}{3}

Schritte zur Lösung

\int_{- 2}^{2} x^{2} + a x^{3} + b x^{4} 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_{- 2}^{2} x^{2} d x + \int_{- 2}^{2} a x^{3} d x + \int_{- 2}^{2} b x^{4} d x

\int_{- 2}^{2} x^{2} d x = \frac{16}{3}

\int_{- 2}^{2} a x^{3} d x = 0

\int_{- 2}^{2} b x^{4} d x = \frac{64 b}{5}

= \frac{16}{3} + 0 + \frac{64 b}{5}

Vereinfache

= \frac{64 b}{5} + \frac{16}{3}

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