integral from 1 to 2 of 3x^3-9x^2+6x

Lösung

\int_{1}^{2} 3 x^{3} - 9 x^{2} + 6 x d x

- \frac{3}{4}

Dezimale

- 0.75

Schritte zur Lösung

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

\int_{1}^{2} 3 x^{3} d x = \frac{45}{4}

\int_{1}^{2} 9 x^{2} d x = 21

\int_{1}^{2} 6 x d x = 9

= \frac{45}{4} - 21 + 9

Vereinfache

\frac{45}{4} - 21 + 9 : - \frac{3}{4}

= - \frac{3}{4}

\int_{0}^{1} x (1 - x^{2})^{9} d x

\int_{0}^{3} 400 - 20 t d t

\int_{1.4}^{1.9} \frac{1}{2} x d x

\int_{4}^{8} 6 x d x

\int_{1}^{- 1} x^{3} d x