de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral from 0 to 1 of x(sqrt(x)-x)

Lösung

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

Lösung

\frac{1}{15}

+1

Dezimale

0.06666 \dots

Schritte zur Lösung

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

Multipliziere aus

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

= \int_{0}^{1} x^{\frac{3}{2}} - x^{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_{0}^{1} x^{\frac{3}{2}} d x - \int_{0}^{1} x^{2} d x

\int_{0}^{1} x^{\frac{3}{2}} d x = \frac{2}{5}

\int_{0}^{1} x^{2} d x = \frac{1}{3}

= \frac{2}{5} - \frac{1}{3}

Vereinfache

\frac{2}{5} - \frac{1}{3} : \frac{1}{15}

= \frac{1}{15}

Graph

Beliebte Beispiele

derivative of ln(sqrt(x-2))

\frac{d}{d x} (ln (x - 2))

integral from 0 to pi of (5e^x+5sin(x))

\int_{0}^{π} (5 e^{x} + 5 sin (x)) d x

derivative f(x)= 1/(2x)

d er i v a t i v e f (x) = \frac{1}{2 x}

(\partial)/(\partial x)(sin(xy^2))

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

derivative (x^2-2)/(e^{2x)}

d er i v a t i v e \frac{x ^{2} - 2}{e ^{2 x}}