integral from 0 to 7 of (2xsqrt(x^2-1))

Lösung

\int_{0}^{7} (2 x x^{2} - 1) d x

1283 + i \frac{2}{3}

Schritte zur Lösung

\int_{0}^{7} 2 x x^{2} - 1 d x

Entferne die Konstante:

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

= 2 \cdot \int_{0}^{7} x x^{2} - 1 d x

Wende U-Substitution an

= 2 \cdot \int_{i}^{43} u^{2} d u

Wende die Potenzregel an

= 2 [\frac{u ^{3}}{3}]_{i}^{43}

Berechne die Grenzen:

643 + \frac{i}{3}

= 2 (643 + \frac{i}{3})

Vereinfache

= 1283 + i \frac{2}{3}

\int_{\frac{π}{3}}^{\frac{π}{6}} tan^{2} (x) d x

\int_{- 1}^{3} e^{x} - 3 d x

\int_{0}^{1} (1 - e^{2})^{\frac{1}{2}} d x

\int_{0}^{2} (\frac{1}{1 + x ^{2}})^{2} d x

\int_{- π}^{π} (sin (x))^{2} d x