zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的微积分 >

integral from-2 to 2 of 1/(x^2+4)

解答

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

解答

\frac{π}{4}

+1

十进制

0.78539 \dots

求解步骤

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

使用换元积分法

= \int_{- 1}^{1} \frac{1}{2 ( u ^{2} + 1 )} d u

提出常数:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int_{- 1}^{1} \frac{1}{u ^{2} + 1} d u

使用积分常见定则:

\int \frac{1}{u ^{2} + 1} d u = arctan (u)

= \frac{1}{2} [arctan (u)]_{- 1}^{1}

带入上下限计算后得:

\frac{π}{2}

= \frac{1}{2} \cdot \frac{π}{2}

化简

= \frac{π}{4}

作图

流行的例子

derivative of e^{2x+5}+1/(e^{x^2})

\frac{d}{d x} (e^{2 x + 5} + \frac{1}{e ^{x^{2}}})

(\partial)/(\partial x)(7xcos(5xy))

\frac{\partial}{\partial x} (7 x cos (5 x y))

xyy^'=4x^2+2y^2

x y y^{^{'}} = 4 x^{2} + 2 y^{2}

derivative of x*y^2

\frac{d}{d x} (x \cdot y^{2})

laplacetransform t^{5/2}

l a pl a ce t r an s f or m t^{\frac{5}{2}}