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 xsqrt(6-x^2)

解答

\int_{0}^{1} x 6 - x^{2} d x

解答

\frac{6 6 - 5 5}{3}

+1

十进制

1.17219 \dots

求解步骤

\int_{0}^{1} x 6 - x^{2} d x

使用换元积分法

= \int_{6}^{5} - \frac{u}{2} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{5}^{6} - \frac{u}{2} 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_{5}^{6} u d u)

使用幂法则

= - (- \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{5}^{6})

化简

= \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{5}^{6}

带入上下限计算后得:

46 - \frac{10 5}{3}

= \frac{1}{2} (46 - \frac{10 5}{3})

化简

= \frac{6 6 - 5 5}{3}

作图

流行的例子

derivative of sin(x+3/4 cot(x))

\frac{d}{d x} (sin (x) + \frac{3}{4} cot (x))

(\partial)/(\partial x)(cos(xy^2))

\frac{\partial}{\partial x} (cos (x y^{2}))

y^{''}+4y=e^{(-t)}

y^{^{''}} + 4 y = e^{(- t)}

derivative csc(sqrt(x+5))

d er i v a t i v e csc (x + 5)

(dy}{dx}-(\frac{1+x)/x)y=(y^2)/x

\frac{d y}{d x} - (\frac{1 + x}{x}) y = \frac{y ^{2}}{x}