integral from 0 to 1 of (7x^2-4x+3)

Lösung

\int_{0}^{1} (7 x^{2} - 4 x + 3) d x

\frac{10}{3}

Dezimale

3.33333 \dots

Schritte zur Lösung

\int_{0}^{1} 7 x^{2} - 4 x + 3 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} 7 x^{2} d x - \int_{0}^{1} 4 x d x + \int_{0}^{1} 3 d x

\int_{0}^{1} 7 x^{2} d x = \frac{7}{3}

\int_{0}^{1} 4 x d x = 2

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

= \frac{7}{3} - 2 + 3

Vereinfache

\frac{7}{3} - 2 + 3 : \frac{10}{3}

= \frac{10}{3}

\int_{- 1}^{\infty} \frac{1}{1 + x ^{2}} d x

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