integral from-1 to 1 of (1+sqrt(1-x^2))

解答

\int_{- 1}^{1} (1 + 1 - x^{2}) d x

2 + \frac{π}{2}

十进制

3.57079 \dots

求解步骤

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

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

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

= 2 + \frac{π}{2}

t^{2} y^{^{''}} + 19 t y^{^{'}} + 162 y = 0

d er i v a t i v e 3 cos (2 u)

n = 2 \sum \infty \frac{1}{n ^{2} + n}

\frac{d}{d x} (- 3 e^{1 - 3 x})

\frac{d}{d x} (2 x + 4)