integral from 1 to 0 of (3x^2+x-5)

Lösung

\int_{1}^{0} (3 x^{2} + x - 5) d x

\frac{7}{2}

Dezimale

3.5

Schritte zur Lösung

\int_{1}^{0} 3 x^{2} + x - 5 d x

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{0}^{1} 3 x^{2} + 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_{0}^{1} 3 x^{2} d x + \int_{0}^{1} x d x - \int_{0}^{1} 5 d x)

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

\int_{0}^{1} x d x = \frac{1}{2}

\int_{0}^{1} 5 d x = 5

= - (1 + \frac{1}{2} - 5)

Vereinfache

- (1 + \frac{1}{2} - 5) : \frac{7}{2}

= \frac{7}{2}

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

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