integral from 7 to 0 of |2x-7|

Lösung

\int_{7}^{0} ∣ 2 x - 7 ∣ d x

- \frac{49}{2}

Dezimale

- 24.5

Schritte zur Lösung

\int_{7}^{0} ∣ 2 x - 7 ∣ d x

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

= - \int_{0}^{7} ∣ 2 x - 7 ∣ d x

Entferne die Extremwerte

= - (\int_{0}^{\frac{7}{2}} - 2 x + 7 d x + \int_{\frac{7}{2}}^{7} 2 x - 7 d x)

\int_{0}^{\frac{7}{2}} - 2 x + 7 d x = \frac{49}{4}

\int_{\frac{7}{2}}^{7} 2 x - 7 d x = \frac{49}{4}

= - (\frac{49}{4} + \frac{49}{4})

Vereinfache

- (\frac{49}{4} + \frac{49}{4}) : - \frac{49}{2}

= - \frac{49}{2}

\int_{0}^{3} 2 x 9 - x^{2} d x

\int_{0}^{\frac{2 π}{3}} sin (x) d x

\int_{0}^{3} 3^{x} + 9 - x^{2} d x

\int_{2 + c o s (x)}^{x^{2} + 1} \frac{1}{x} d x

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