integral from 0 to 1 of 6x-x^2

Lösung

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

\frac{8}{3}

Dezimale

2.66666 \dots

Schritte zur Lösung

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

\int_{0}^{1} 6 x d x = 3

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

= 3 - \frac{1}{3}

Vereinfache

3 - \frac{1}{3} : \frac{8}{3}

= \frac{8}{3}

\int_{0}^{2} y x + 2 d x

\int_{0}^{4} (\frac{x}{1 + x ^{4}}) d x

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

\int_{0}^{1} sin (y^{2}) y d y

\int_{o}^{t} t d t