integral from 1 to 2 of 1/2 x^2

Lösung

\int_{1}^{2} \frac{1}{2} x^{2} d x

\frac{7}{6}

Dezimale

1.16666 \dots

Schritte zur Lösung

\int_{1}^{2} \frac{1}{2} x^{2} d x

Entferne die Konstante:

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

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

Wende die Potenzregel an

= \frac{1}{2} [\frac{x ^{3}}{3}]_{1}^{2}

Berechne die Grenzen:

\frac{7}{3}

= \frac{1}{2} \cdot \frac{7}{3}

Vereinfache

= \frac{7}{6}

\int_{- 1}^{1} x^{2} (x^{3} + 3)^{4} d x

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

\int_{1}^{3} 25 - (t - 5)^{2} d t

\int_{1}^{4} \frac{4}{x} d x

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