integral from 2 to B of (2x-3)^4

Lösung

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

\frac{16 B ^{5} - 120 B ^{4} + 360 B ^{3} - 540 B ^{2} + 405 B - 122}{5}

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{1}^{2 B - 3} \frac{u ^{4}}{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_{1}^{2 B - 3} u^{4} d u

Wende die Potenzregel an

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

Berechne die Grenzen:

\frac{( 2 B - 3 ) ^{5}}{5} - \frac{1}{5}

= \frac{1}{2} (\frac{( 2 B - 3 ) ^{5}}{5} - \frac{1}{5})

Vereinfache

= \frac{16 B ^{5} - 120 B ^{4} + 360 B ^{3} - 540 B ^{2} + 405 B - 122}{5}

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