integral from 1 to 4 of (1+x)/(sqrt(x))

Lösung

\int_{1}^{4} \frac{1 + x}{x} d x

\frac{20}{3}

Dezimale

6.66666 \dots

Schritte zur Lösung

\int_{1}^{4} \frac{1 + x}{x} d x

Multipliziere aus

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

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

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

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

= 2 + \frac{14}{3}

Vereinfache

2 + \frac{14}{3} : \frac{20}{3}

= \frac{20}{3}

\int_{0}^{\frac{1}{2}} x cos (\frac{πk x}{2}) d x

\int_{0}^{3} 3 y - y^{2} d y

\int_{0}^{2 x} cos (x^{2}) d x

\int_{0}^{π} x ∣ cos (x) ∣ d x

\int_{0}^{1} x \frac{x}{1 - x} d x