integral from 1 to 4 of (x-7)/(sqrt(x))

Lösung

\int_{1}^{4} \frac{x - 7}{x} d x

- \frac{28}{3}

Dezimale

- 9.33333 \dots

Schritte zur Lösung

\int_{1}^{4} \frac{x - 7}{x} d x

Multipliziere aus

\frac{x - 7}{x} : x - \frac{7}{x}

= \int_{1}^{4} x - \frac{7}{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{7}{x} d x

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

\int_{1}^{4} \frac{7}{x} d x = 14

= \frac{14}{3} - 14

Vereinfache

\frac{14}{3} - 14 : - \frac{28}{3}

= - \frac{28}{3}

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

\frac{d}{d x} ((11 x^{4} + 5)^{3})

\int x sec^{2} (9 x) d x

\frac{\partial}{\partial y} (x cos (x + y))

\frac{d y}{d x} + 2 y = 20 e^{3 x}