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Beliebt Rechnen >

integral from 0 to 1 of rsqrt(1-r^2)

Lösung

\int_{0}^{1} r 1 - r^{2} d r

Lösung

\frac{1}{3}

+1

Dezimale

0.33333 \dots

Schritte zur Lösung

\int_{0}^{1} r 1 - r^{2} d r

Wende U-Substitution an

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

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

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

Entferne die Konstante:

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

= - (- \int_{0}^{1} u^{2} d u)

Wende die Potenzregel an

= - (- [\frac{u ^{3}}{3}]_{0}^{1})

Vereinfache

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

Berechne die Grenzen:

\frac{1}{3}

= \frac{1}{3}

Graph

Beliebte Beispiele

integral of ((x^3)/(x-1))

\int (\frac{x ^{3}}{x - 1}) d x

derivative of (1-x^3-3x(1-x)^2)

\frac{d}{d x} ((1 - x)^{3} - 3 x (1 - x)^{2})

(dy)/(dx)=(x-1)/(3x^2-6x-1)

\frac{d y}{d x} = \frac{x - 1}{3 x ^{2} - 6 x - 1}

integral of (ln(x))2

\int (ln (x)) 2 d x

derivative (ln(x))/(ln(2))

d er i v a t i v e \frac{ln ( x )}{ln ( 2 )}