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 2x*sqrt(1+4x^2)

解答

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

解答

\frac{5 5 - 1}{6}

+1

十进制

1.69672 \dots

求解步骤

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

提出常数:

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

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

使用换元积分法

= 2 \cdot \int_{1}^{5} \frac{u}{8} d u

提出常数:

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

= 2 \cdot \frac{1}{8} \cdot \int_{1}^{5} u d u

使用幂法则

= 2 \cdot \frac{1}{8} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{5}

化简

2 \cdot \frac{1}{8} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{5} : \frac{1}{4} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{5}

= \frac{1}{4} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{5}

带入上下限计算后得:

\frac{10 5}{3} - \frac{2}{3}

= \frac{1}{4} (\frac{10 5}{3} - \frac{2}{3})

化简

= \frac{5 5 - 1}{6}

作图

流行的例子

integral of ((7-x))/((x^2-4x+4))

\int \frac{( 7 - x )}{( x ^{2} - 4 x + 4 )} d x

integral of 5xcos(4x)

\int 5 x cos (4 x) d x

derivative of (cos(x)/(1-sin(x)))

\frac{d}{d x} (\frac{cos ( x )}{1 - sin ( x )})

integral of sin^3(cos^2(x)

\int sin^{3} (cos^{2} (d) x) d x

integral of (14x^6y^{-4}-12x^5y^{-3})

\int (14 x^{6} y^{- 4} - 12 x^{5} y^{- 3}) d x