integral of 1/2-1/4 |x-3|

Lösung

\int \frac{1}{2} - \frac{1}{4} ∣ x - 3 ∣ d x

\frac{1}{2} x - \frac{1}{8} ∣ x - 3 ∣ (x - 3) + C

Schritte zur Lösung

\int \frac{1}{2} - \frac{1}{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 \frac{1}{2} d x - \int \frac{1}{4} ∣ x - 3 ∣ d x

\int \frac{1}{2} d x = \frac{1}{2} x

\int \frac{1}{4} ∣ x - 3 ∣ d x = \frac{1}{8} ∣ x - 3 ∣ (x - 3)

= \frac{1}{2} x - \frac{1}{8} ∣ x - 3 ∣ (x - 3)

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} x - \frac{1}{8} ∣ x - 3 ∣ (x - 3) + C

t an g e n t y = (3 x + \frac{1}{x})^{2}, (1, 16)

\int sec^{2} (x) (cos^{3} (x) + 1) d x

x \to 1 + lim (ln (x - 1))

\int_{0}^{\infty} e^{- 4 t} d t

d er i v a t i v e π^{4}