integral from 0 to 1 of [(x^2-1)-(-x+2)]

Lösung

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

- \frac{13}{6}

Dezimale

- 2.16666 \dots

Schritte zur Lösung

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

Vereinfache

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

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

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

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

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

Vereinfache

\frac{1}{3} + \frac{1}{2} - 3 : - \frac{13}{6}

= - \frac{13}{6}

\int 2 x (x^{2} + 2)^{5} d x

\frac{d}{d x} (\frac{5 x}{4})

x \to 0 lim (x ln (x - 1))

a re a x^{2} - 2 x + 1, - x + 3

sec^{2} (x) d y + csc (y) d x = 0