integral from 0 to 1 of sqrt(2x+3)

Lösung

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

\frac{5 5 - 3 3}{3}

Dezimale

1.99472 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{3}^{5} \frac{u}{2} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{3}^{5} u d u

Wende die Potenzregel an

= \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{3}^{5}

Berechne die Grenzen:

\frac{10 5}{3} - 23

= \frac{1}{2} (\frac{10 5}{3} - 23)

Vereinfache

= \frac{5 5 - 3 3}{3}

\int_{0}^{1} (4 + 3 x^{2}) d x

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

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