integral from 0 to 2 of xsqrt(1-x^2)

Lösung

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

3 i + \frac{1}{3}

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{1}^{3 i} - u^{2} d u

Entferne die Konstante:

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

= - \int_{1}^{3 i} u^{2} d u

Wende die Potenzregel an

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

Berechne die Grenzen:

- 3 i - \frac{1}{3}

= - (- 3 i - \frac{1}{3})

Vereinfache

= 3 i + \frac{1}{3}

\int_{0}^{θ} x (\frac{2 x}{θ ^{2}}) d x

\int_{- 1}^{1} - x^{2} + 2 d x

\int_{- 4}^{2} \frac{2 x}{3 x ^{2} + 10} d x

\int_{0}^{3} \frac{9 - x ^{2}}{3} d x

\int_{4}^{8} x^{3} d x