integral from-1 to 3 of (x^2+3)^3

Lösung

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

\frac{38912}{35}

Dezimale

1111.77142 \dots

Schritte zur Lösung

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

Multipliziere aus

(x^{2} + 3)^{3} : x^{6} + 9 x^{4} + 27 x^{2} + 27

= \int_{- 1}^{3} x^{6} + 9 x^{4} + 27 x^{2} + 27 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_{- 1}^{3} x^{6} d x + \int_{- 1}^{3} 9 x^{4} d x + \int_{- 1}^{3} 27 x^{2} d x + \int_{- 1}^{3} 27 d x

\int_{- 1}^{3} x^{6} d x = \frac{2188}{7}

\int_{- 1}^{3} 9 x^{4} d x = \frac{2196}{5}

\int_{- 1}^{3} 27 x^{2} d x = 252

\int_{- 1}^{3} 27 d x = 108

= \frac{2188}{7} + \frac{2196}{5} + 252 + 108

Vereinfache

\frac{2188}{7} + \frac{2196}{5} + 252 + 108 : \frac{38912}{35}

= \frac{38912}{35}