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Beliebt Rechnen >

integral from 0 to 2 of y/(sqrt(9-y^2))

Lösung

\int_{0}^{2} \frac{y}{9 - y ^{2}} d y

Lösung

3 - 5

+1

Dezimale

0.76393 \dots

Schritte zur Lösung

\int_{0}^{2} \frac{y}{9 - y ^{2}} d y

Wende U-Substitution an

= \int_{9}^{5} - \frac{1}{2 u} d u

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

= - \int_{5}^{9} - \frac{1}{2 u} d u

Entferne die Konstante:

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

= - (- \frac{1}{2} \cdot \int_{5}^{9} \frac{1}{u} d u)

Wende die Potenzregel an

= - (- \frac{1}{2} [2 u^{\frac{1}{2}}]_{5}^{9})

Vereinfache

- (- \frac{1}{2} [2 u^{\frac{1}{2}}]_{5}^{9}) : \frac{1}{2} [2 u]_{5}^{9}

= \frac{1}{2} [2 u]_{5}^{9}

Berechne die Grenzen:

6 - 25

= \frac{1}{2} (6 - 25)

Vereinfache

= 3 - 5

Graph

Beliebte Beispiele

integral of ((5x+3))/(x^3-2x^2-3x)

\int \frac{( 5 x + 3 )}{x ^{3} - 2 x ^{2} - 3 x} d x

y^{^{'}} = x^{2} \cdot y

(\partial)/(\partial x)(ln(x^6+y^3))

\frac{\partial}{\partial x} (ln (x^{6} + y^{3}))

taylor sin(x) pi/4

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integral of sec^2(11x)

\int sec^{2} (11 x) d x