integral from 0 to 1 of 1/(sqrt(4-3x^2))

Lösung

\int_{0}^{1} \frac{1}{4 - 3 x ^{2}} d x

\frac{π}{3 3}

Dezimale

0.60459 \dots

Schritte zur Lösung

\int_{0}^{1} \frac{1}{4 - 3 x ^{2}} d x

Trigonometrische Substitution anwenden

= \int_{0}^{\frac{π}{3}} \frac{1}{3} d u

Entferne die Konstante:

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

= \frac{1}{3} \cdot \int_{0}^{\frac{π}{3}} 1 d u

Integral einer Konstanten :

\int a d x = a x

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

Vereinfache

= \frac{1}{3} [u]_{0}^{\frac{π}{3}}

Berechne die Grenzen:

\frac{π}{3}

= \frac{1}{3} \cdot \frac{π}{3}

Vereinfache

= \frac{π}{3 3}

\int_{- 1}^{0} (2 y + 2) d y

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