integral from 1 to 4 of (x-2)/(sqrt(x))

Lösung

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

\frac{2}{3}

Dezimale

0.66666 \dots

Schritte zur Lösung

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

Multipliziere aus

\frac{x - 2}{x} : x - \frac{2}{x}

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

\int_{1}^{4} x d x = \frac{14}{3}

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

= \frac{14}{3} - 4

Vereinfache

\frac{14}{3} - 4 : \frac{2}{3}

= \frac{2}{3}

d er i v a t i v e f (x) = 3 arccsc (x)

\int x^{2} sech^{2} (x^{3}) d x

\frac{d}{d x} (x^{3} - 8)

y^{^{'}} + 2 y = 25 sin (x) + 40 cos (x), y (0) = 1

t an g e n t y = x, (9, 3)