integral from 1 to 4 of (3/x-x^{-1/2})

Lösung

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

6 ln (2) - 2

Dezimale

2.15888 \dots

Schritte zur Lösung

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

\int_{1}^{4} \frac{3}{x} d x = 6 ln (2)

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

= 6 ln (2) - 2

\int_{- 1.5}^{1} (2 x^{2} + x - 3) d x

\int_{- 2}^{3} x^{3} ln (e^{x}) d x

\int_{1}^{e^{7}} \frac{4 ln ( x )}{x} d x

\int_{0}^{5} 6 x^{2} d x

\int_{1}^{8} x^{- \frac{7}{3}} d x