integral from 0 to 5 of 1/4 (5-x)sqrt(x)

Lösung

\int_{0}^{5} \frac{1}{4} (5 - x) x d x

\frac{5 5}{3}

Dezimale

3.72677 \dots

Schritte zur Lösung

\int_{0}^{5} \frac{1}{4} (5 - x) x d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{4} \cdot \int_{0}^{5} (5 - x) x d x

Multipliziere aus

(5 - x) x : 5 x - x^{\frac{3}{2}}

= \frac{1}{4} \cdot \int_{0}^{5} 5 x - x^{\frac{3}{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

= \frac{1}{4} (\int_{0}^{5} 5 x d x - \int_{0}^{5} x^{\frac{3}{2}} d x)

\int_{0}^{5} 5 x d x = \frac{50 5}{3}

\int_{0}^{5} x^{\frac{3}{2}} d x = 105

= \frac{1}{4} (\frac{50 5}{3} - 105)

Vereinfache

\frac{1}{4} (\frac{50 5}{3} - 105) : \frac{5 5}{3}

= \frac{5 5}{3}

\frac{d}{d t} (v (t) t)

\frac{\partial}{\partial x} (x^{2} - 2 x y)

\int \frac{4 + x ^{2}}{x} d x

x \to - 3 lim (x^{2} - 9)

x \to 7 - lim (\frac{2}{x + 7})