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Beliebt Rechnen >

integral from 4 to 5 of xsqrt(25-x^2)

Lösung

\int_{4}^{5} x 25 - x^{2} d x

Lösung

9

Schritte zur Lösung

\int_{4}^{5} x 25 - x^{2} d x

Wende U-Substitution an

= \int_{9}^{0} - \frac{u}{2} d u

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

= - \int_{0}^{9} - \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_{0}^{9} u d u)

Wende die Potenzregel an

= - (- \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{9})

Vereinfache

= \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{9}

Berechne die Grenzen:

18

= \frac{1}{2} \cdot 18

Vereinfache

= 9

Graph

Beliebte Beispiele

integral of (e^{-y})

\int (e^{- y}) d y

x^'=(1-x)*0.03-((0.03x))/((e^3-1))

x^{^{'}} = (1 - x) \cdot 0.03 - \frac{( 0.03 x )}{( e ^{3} - 1 )}

y^'-(2y)/x =-x^2y^2

y^{^{'}} - \frac{2 y}{x} = - x^{2} y^{2}

integral of (ax)/(x^4+b^4)

\int \frac{a x}{x ^{4} + b ^{4}} d x

limit as x approaches 0 of (-1)/(5x)

x \to 0 lim (\frac{- 1}{5 x})