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

Lösung

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

\frac{8}{3}

Dezimale

2.66666 \dots

Schritte zur Lösung

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

Multipliziere aus

(3 - x)^{2} : 9 - 6 x + x^{2}

= \int_{1}^{3} 9 - 6 x + x^{2} 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_{1}^{3} 9 d x - \int_{1}^{3} 6 x d x + \int_{1}^{3} x^{2} d x

\int_{1}^{3} 9 d x = 18

\int_{1}^{3} 6 x d x = 24

\int_{1}^{3} x^{2} d x = \frac{26}{3}

= 18 - 24 + \frac{26}{3}

Vereinfache

18 - 24 + \frac{26}{3} : \frac{8}{3}

= \frac{8}{3}

\int 4 x^{3} + 2 x y^{2} ln (x^{2} + y^{2}) d x

(x^{2} - x y) d x + x d y = 0

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n = 0 \sum \infty \frac{7}{5 ^{n}}

\int - 7 sec (2 x) tan (2 x) d x