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

Lösung

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

\frac{8}{3}

Dezimale

2.66666 \dots

Schritte zur Lösung

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

Vereinfache

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

\int_{- 1}^{1} 2 d x = 4

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

= 4 - \frac{4}{3}

Vereinfache

4 - \frac{4}{3} : \frac{8}{3}

= \frac{8}{3}

\int_{\frac{π}{3}}^{\frac{π}{2}} cos (π) x d x

\int_{0}^{π} (sin (t) cos (t)) d t

\int_{0}^{1} (2 x + 3)^{10} d x

\int_{0}^{1} \frac{1 - x ^{2}}{4} d x

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