integral from 0 to 1 of (7-21/2 x)^2

Lösung

\int_{0}^{1} (7 - \frac{21}{2} x)^{2} d x

\frac{49}{4}

Dezimale

12.25

Schritte zur Lösung

\int_{0}^{1} (7 - \frac{21}{2} x)^{2} d x

Vereinfache

(7 - \frac{21}{2} x)^{2} : 49 - 147 x + \frac{441}{4} x^{2}

= \int_{0}^{1} 49 - 147 x + \frac{441}{4} 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_{0}^{1} 49 d x - \int_{0}^{1} 147 x d x + \int_{0}^{1} \frac{441}{4} x^{2} d x

\int_{0}^{1} 49 d x = 49

\int_{0}^{1} 147 x d x = \frac{147}{2}

\int_{0}^{1} \frac{441}{4} x^{2} d x = \frac{147}{4}

= 49 - \frac{147}{2} + \frac{147}{4}

Vereinfache

49 - \frac{147}{2} + \frac{147}{4} : \frac{49}{4}

= \frac{49}{4}

\int_{0}^{14} 8 x d x

\int_{0}^{4} 3 - \frac{x}{4} d x

\int_{- 1}^{5} k x^{2} d x

\int_{0}^{2} x^{3} \cdot e^{x^{4}} d x

\int_{1}^{5} (x - \frac{5}{x})^{2} d x