integral from 0 to 1 of (x+2)(x-3)

Lösung

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

- \frac{37}{6}

Dezimale

- 6.16666 \dots

Schritte zur Lösung

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

Multipliziere aus

(x + 2) (x - 3) : x^{2} - x - 6

= \int_{0}^{1} x^{2} - x - 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_{0}^{1} x^{2} d x - \int_{0}^{1} x d x - \int_{0}^{1} 6 d x

\int_{0}^{1} x^{2} d x = \frac{1}{3}

\int_{0}^{1} x d x = \frac{1}{2}

\int_{0}^{1} 6 d x = 6

= \frac{1}{3} - \frac{1}{2} - 6

Vereinfache

\frac{1}{3} - \frac{1}{2} - 6 : - \frac{37}{6}

= - \frac{37}{6}

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

\int_{0}^{1} \frac{6}{5} (x + y^{2}) d y

\int_{4}^{5} 3 x x - 4 d x

\int_{1}^{4} (2 x + 3) d x

\int_{- 1}^{0} 1 - x^{2} d x