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

Lösung

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

\frac{125}{6}

Dezimale

20.83333 \dots

Schritte zur Lösung

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

\int_{- 2}^{3} x d x = \frac{5}{2}

\int_{- 2}^{3} x^{2} d x = \frac{35}{3}

\int_{- 2}^{3} 6 d x = 30

= \frac{5}{2} - \frac{35}{3} + 30

Vereinfache

\frac{5}{2} - \frac{35}{3} + 30 : \frac{125}{6}

= \frac{125}{6}

\int_{0}^{1} x y e^{x y^{2}} d y

\int_{0}^{1} \frac{6}{7} (x^{2} + \frac{x y}{2}) d x

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

\int_{- 5}^{1} x^{2} + 4 x - 5 d x

\int_{0}^{1} x 3 x^{2} + 1 d x