integral from-infinity to 0 of 1/(9+x^2)

解答

\int_{- \infty}^{0} \frac{1}{9 + x ^{2}} d x

\frac{π}{6}

十进制

0.52359 \dots

求解步骤

\int_{- \infty}^{0} \frac{1}{9 + x ^{2}} d x

计算不定积分:

\int \frac{1}{9 + x ^{2}} d x = \frac{1}{3} arctan (\frac{x}{3}) + C

带入上下限计算后得:

\int_{- \infty}^{0} \frac{1}{9 + x ^{2}} d x = 0 - (- \frac{π}{6})

= 0 - (- \frac{π}{6})

化简

= \frac{π}{6}

s l o p e (- 1, 4), (5, - 1)

y^{^{'}} = ry ln (\frac{k}{y})

x \to + 5 + lim (x - 5)

\frac{\partial}{\partial x} (ln (6 x^{2} + y^{2} + 4))

t an g e n t y = x^{2} - 4 x + 4, (3, 1)