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 0 to 1 of x^5sqrt(1+4x^2)

解答

\int_{0}^{1} x^{5} 1 + 4 x^{2} d x

解答

\frac{- 1 + 125 5}{840}

+1

十进制

0.33155 \dots

求解步骤

\int_{0}^{1} x^{5} 1 + 4 x^{2} d x

乘以

1 + 4 x^{2}

的共轭根式

: \frac{1 - 16 x ^{4}}{1 - 4 x ^{2}}

= \int_{0}^{1} x^{5} \frac{1 - 16 x ^{4}}{1 - 4 x ^{2}} d x

找到无定义的点（奇点）:

x = \frac{1}{2}

如果存在

b, a < b < c, f (b) =

无定义

, \int_{a}^{c} f (x) d x = \int_{a}^{b} f (x) d x + \int_{b}^{c} f (x) d x

= \int_{0}^{\frac{1}{2}} x^{5} \frac{1 - 16 x ^{4}}{1 - 4 x ^{2}} d x + \int_{\frac{1}{2}}^{1} x^{5} \frac{1 - 16 x ^{4}}{1 - 4 x ^{2}} d x

\int_{0}^{\frac{1}{2}} x^{5} \frac{1 - 16 x ^{4}}{1 - 4 x ^{2}} d x = \frac{11 2 - 4}{3360}

\int_{\frac{1}{2}}^{1} x^{5} \frac{1 - 16 x ^{4}}{1 - 4 x ^{2}} d x = \frac{- 11 2 + 500 5}{3360}

= \frac{11 2 - 4}{3360} + \frac{- 11 2 + 500 5}{3360}

化简

\frac{11 2 - 4}{3360} + \frac{- 11 2 + 500 5}{3360} : \frac{- 1 + 125 5}{840}

= \frac{- 1 + 125 5}{840}

作图

流行的例子

integral from-1 to 2 of sqrt(|x|-x)

\int_{- 1}^{2} ∣ x ∣ - x d x

integral from 0 to x of 7e^{-7x}

\int_{0}^{x} 7 e^{- 7 x} d x

integral from 2 to 5 of 1/(sqrt(x))

\int_{2}^{5} \frac{1}{x} d x

integral from-1 to 5 of sqrt(2x+6)

\int_{- 1}^{5} 2 x + 6 d x

integral from 1 to 2 of 3^x+1/x

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