integral from 1/2 to 2 of 2/x-1/2 x

Lösung

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

4 ln (2) - \frac{15}{16}

Dezimale

1.83508 \dots

Schritte zur Lösung

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

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

\int_{\frac{1}{2}}^{2} \frac{1}{2} x d x = \frac{15}{16}

= 4 ln (2) - \frac{15}{16}

\int \frac{4 - 32 x}{81 - 16 x ^{2}} d x

x \to 3 lim (\frac{9 + x}{3 - x})

d er i v a t i v e f (x) = - x^{2} - 3 x + 4

y^{^{'}} + x^{2} y = 1

ma c l a u r in \frac{- sin ( x ) 2 x}{3}