integral of 4-|x|

解答

\int 4 - ∣ x ∣ d x

4 x - \frac{x ∣ x ∣}{2} + C

求解步骤

\int 4 - ∣ x ∣ d x

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 4 d x - \int ∣ x ∣ d x

\int 4 d x = 4 x

\int ∣ x ∣ d x = \frac{x ∣ x ∣}{2}

= 4 x - \frac{x ∣ x ∣}{2}

解答补常数

= 4 x - \frac{x ∣ x ∣}{2} + C

\int_{- 1}^{1} x + 1 - 1 d x

\int_{- 3}^{2} ∣ x + 1 ∣ d x

x \to 1 lim (\frac{2 x}{ln ( x )})

d er i v a t i v e f (x) = 6 - x

\int_{0}^{2} e^{\frac{x}{2}} d x