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 4 of xsqrt(25-x^2)

解答

\int_{0}^{4} x 25 - x^{2} d x

解答

\frac{98}{3}

+1

十进制

32.66666 \dots

求解步骤

\int_{0}^{4} x 25 - x^{2} d x

使用换元积分法

= \int_{25}^{9} - \frac{u}{2} d u

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

= - \int_{9}^{25} - \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_{9}^{25} u d u)

使用幂法则

= - (- \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{9}^{25})

化简

= \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{9}^{25}

带入上下限计算后得:

\frac{196}{3}

= \frac{1}{2} \cdot \frac{196}{3}

化简

= \frac{98}{3}

作图

流行的例子

integral from x to 1 of (x+y)

\int_{x}^{1} (x + y) d y

integral from 1 to 2 of (3x-5x+1)

\int_{1}^{2} (3 x - 5 x + 1) d x

integral from 0 to sin(x) of 2sqrt(t)

\int_{0}^{s i n (x)} 2 t d t

integral from 0 to pi of (3e^x+8sin(x))

\int_{0}^{π} (3 e^{x} + 8 sin (x)) d x

integral from 2 to 4 of-6/(x^2)

\int_{2}^{4} - \frac{6}{x ^{2}} d x