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Beliebt Rechnen >

integral from 0 to 2 of 2/(sqrt(8-x^2))

Lösung

\int_{0}^{2} \frac{2}{8 - x ^{2}} d x

Lösung

\frac{π}{2}

+1

Dezimale

1.57079 \dots

Schritte zur Lösung

\int_{0}^{2} \frac{2}{8 - x ^{2}} d x

Entferne die Konstante:

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

= 2 \cdot \int_{0}^{2} \frac{1}{8 - x ^{2}} d x

Trigonometrische Substitution anwenden

= 2 \cdot \int_{0}^{\frac{π}{4}} 1 d u

Integral einer Konstanten :

\int a d x = a x

= 2 [1 \cdot u]_{0}^{\frac{π}{4}}

Vereinfache

= 2 [u]_{0}^{\frac{π}{4}}

Berechne die Grenzen:

\frac{π}{4}

= 2 \cdot \frac{π}{4}

Vereinfache

= \frac{π}{2}

Graph

Beliebte Beispiele

derivative of sqrt(cos(x+1))

\frac{d}{d x} (cos (x) + 1)

(d^2)/(dx^2)(5ln(x^5))

\frac{d ^{2}}{d x ^{2}} (5 ln (x^{5}))

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

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

fläche sin(x),cos(x)-1

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integral from 1 to 5 of x^3-10x^2+29x-20

\int_{1}^{5} x^{3} - 10 x^{2} + 29 x - 20 d x