integral from 1 to 2 of (x+1)/(sqrt(x))

Lösung

\int_{1}^{2} \frac{x + 1}{x} d x

\frac{4 2 - 2}{3} + 22 - 2

Dezimale

2.04737 \dots

Schritte zur Lösung

\int_{1}^{2} \frac{x + 1}{x} d x

Multipliziere aus

\frac{x + 1}{x} : x + \frac{1}{x}

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

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

\int_{1}^{2} \frac{1}{x} d x = 22 - 2

= \frac{4 2 - 2}{3} + 22 - 2

\frac{d ^{4} y}{d x ^{4}} - 23 \frac{d ^{2} y}{d x ^{2}} - 50 y = 0

x \to 0 lim (sin (2 x))

in v erse l a pl a ce \frac{s}{( s - 2 ) ^{2} + 16}

\int_{\frac{1}{3}}^{5} 16 x ln (3 x) d x

t an g e n t f (x) = x^{2} + 4 x - 5, at x = 2