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 r of xsqrt(r^2-x^2)

Lösung

\int_{0}^{r} x r^{2} - x^{2} d x

Lösung

\frac{( r ^{2} ) ^{\frac{3}{2}}}{3}

Schritte zur Lösung

\int_{0}^{r} x r^{2} - x^{2} d x

Wende U-Substitution an

= \int_{r^{2}}^{0} - \frac{u}{2} d u

Entferne die Konstante:

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

= - \frac{1}{2} \cdot \int_{r^{2}}^{0} u d u

Wende die Potenzregel an

= - \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{r^{2}}^{0}

Berechne die Grenzen:

- \frac{2}{3} (r^{2})^{\frac{3}{2}}

= - \frac{1}{2} (- \frac{2}{3} (r^{2})^{\frac{3}{2}})

Vereinfache

= \frac{( r ^{2} ) ^{\frac{3}{2}}}{3}

Beliebte Beispiele

integral of x/((x^2-4)(x+3))

\int \frac{x}{( x ^{2} - 4 ) ( x + 3 )} d x

integral of 15^x

\int 1 5^{x} d x

tangent f(x)= 5/(2sqrt(5x+6)),\at x=2

t an g e n t f (x) = \frac{5}{2 5 x + 6}, at x = 2

integral of ze^z

\int z e^{z} d z

derivative y=sqrt(10+cot^2(x))

d er i v a t i v e y = 10 + cot^{2} (x)