integral from-1 to 4 of (4x-3)(x-3)

Lösung

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

\frac{115}{6}

Dezimale

19.16666 \dots

Schritte zur Lösung

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

Wende die partielle Integration an

= [(4 x - 3) (\frac{x ^{2}}{2} - 3 x) - \int 4 (\frac{x ^{2}}{2} - 3 x) d x]_{- 1}^{4}

\int 4 (\frac{x ^{2}}{2} - 3 x) d x = 4 (\frac{x ^{3}}{6} - \frac{3 x ^{2}}{2})

= [(4 x - 3) (\frac{x ^{2}}{2} - 3 x) - 4 (\frac{x ^{3}}{6} - \frac{3 x ^{2}}{2})]_{- 1}^{4}

Vereinfache

[(4 x - 3) (\frac{x ^{2}}{2} - 3 x) - 4 (\frac{x ^{3}}{6} - \frac{3 x ^{2}}{2})]_{- 1}^{4} : [\frac{1}{6} (8 x^{3} - 45 x^{2} + 54 x)]_{- 1}^{4}

= [\frac{1}{6} (8 x^{3} - 45 x^{2} + 54 x)]_{- 1}^{4}

Berechne die Grenzen:

\frac{115}{6}

= \frac{115}{6}

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