integral from 0 to 1 of 4x(x^2+3)^3

Lösung

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

\frac{175}{2}

Dezimale

87.5

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende U-Substitution an

= 4 \cdot \int_{3}^{4} \frac{u ^{3}}{2} d u

Entferne die Konstante:

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

= 4 \cdot \frac{1}{2} \cdot \int_{3}^{4} u^{3} d u

Wende die Potenzregel an

= 4 \cdot \frac{1}{2} [\frac{u ^{4}}{4}]_{3}^{4}

Vereinfache

4 \cdot \frac{1}{2} [\frac{u ^{4}}{4}]_{3}^{4} : 2 [\frac{u ^{4}}{4}]_{3}^{4}

= 2 [\frac{u ^{4}}{4}]_{3}^{4}

Berechne die Grenzen:

\frac{175}{4}

= 2 \cdot \frac{175}{4}

Vereinfache

= \frac{175}{2}

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