integral from-2 to 2 of |x^2-1|

解答

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

4

求解步骤

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

拿掉绝对值

= \int_{- 2}^{- 1} x^{2} - 1 d x + \int_{- 1}^{1} - x^{2} + 1 d x + \int_{1}^{2} x^{2} - 1 d x

\int_{- 2}^{- 1} x^{2} - 1 d x = \frac{4}{3}

\int_{- 1}^{1} - x^{2} + 1 d x = \frac{4}{3}

\int_{1}^{2} x^{2} - 1 d x = \frac{4}{3}

= \frac{4}{3} + \frac{4}{3} + \frac{4}{3}

化简

\frac{4}{3} + \frac{4}{3} + \frac{4}{3} : 4

= 4

\int 4 x x^{2} + 2 x d x

\frac{d}{d x} (ln (3 x^{2} + 2 x - 1))

d er i v a t i v e y = sin^{5} (2 x + 1)

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

\frac{d}{d x} (3 x^{2} + x + 1)