integral from 0 to 4 of x^3-10x^2+24x

Lösung

\int_{0}^{4} x^{3} - 10 x^{2} + 24 x d x

\frac{128}{3}

Dezimale

42.66666 \dots

Schritte zur Lösung

\int_{0}^{4} x^{3} - 10 x^{2} + 24 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} x^{3} d x - \int_{0}^{4} 10 x^{2} d x + \int_{0}^{4} 24 x d x

\int_{0}^{4} x^{3} d x = 64

\int_{0}^{4} 10 x^{2} d x = \frac{640}{3}

\int_{0}^{4} 24 x d x = 192

= 64 - \frac{640}{3} + 192

Vereinfache

64 - \frac{640}{3} + 192 : \frac{128}{3}

= \frac{128}{3}

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

\int_{9}^{10} (x x - 9) d x

\int_{- 3}^{3} 7 + 2 t^{2} (8 t) d t

\int_{0}^{1} e^{3 t} d t

\int_{0}^{2 π} 4 cos (t) sin (t) d t