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

Lösung

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

\frac{4}{3}

Dezimale

1.33333 \dots

Schritte zur Lösung

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

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{- 1}^{1} x^{2} - 1 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}^{1} x^{2} d x - \int_{- 1}^{1} 1 d x)

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

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

= - (\frac{2}{3} - 2)

Vereinfache

- (\frac{2}{3} - 2) : \frac{4}{3}

= \frac{4}{3}

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

\int_{0}^{3} e^{t^{2}} d t

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

\int_{0}^{9} 3 - x d x

\int_{0}^{1} z^{4} 1 - z^{2} d z