integral from 2 to x of (x^2+3x-5)

Lösung

\int_{2}^{x} (x^{2} + 3 x - 5) d x

\frac{1}{3} (x^{3} - 8) + \frac{3 x ^{2}}{2} - 5 x + 4

Schritte zur Lösung

\int_{2}^{x} x^{2} + 3 x - 5 d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{2}^{x} x^{2} d x + \int_{2}^{x} 3 x d x - \int_{2}^{x} 5 d x

\int_{2}^{x} x^{2} d x = \frac{x ^{3} - 8}{3}

\int_{2}^{x} 3 x d x = 3 (\frac{x ^{2}}{2} - 2)

\int_{2}^{x} 5 d x = 5 x - 10

= \frac{x ^{3} - 8}{3} + 3 (\frac{x ^{2}}{2} - 2) - (5 x - 10)

Vereinfache

\frac{x ^{3} - 8}{3} + 3 (\frac{x ^{2}}{2} - 2) - (5 x - 10) : \frac{1}{3} (x^{3} - 8) + \frac{3 x ^{2}}{2} - 5 x + 4

= \frac{1}{3} (x^{3} - 8) + \frac{3 x ^{2}}{2} - 5 x + 4

\int_{0}^{8} 3 x^{2} - 36 x + 105 d x

\int_{0}^{\frac{π}{6}} cos (3 A)

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

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