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 (xcos(x^2))/2

解答

\int_{0}^{4} \frac{x cos ( x ^{2} )}{2} d x

解答

\frac{1}{4} sin (16)

+1

十进制

- 0.07197 \dots

求解步骤

\int_{0}^{4} \frac{x cos ( x ^{2} )}{2} d x

提出常数:

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

= \frac{1}{2} \cdot \int_{0}^{4} x cos (x^{2}) d x

使用换元积分法

= \frac{1}{2} \cdot \int_{0}^{16} \frac{cos ( 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 \frac{1}{2} \cdot \int_{0}^{16} cos (u) d u

使用积分常见定则:

\int cos (u) d u = sin (u)

= \frac{1}{2} \cdot \frac{1}{2} [sin (u)]_{0}^{16}

化简

\frac{1}{2} \cdot \frac{1}{2} [sin (u)]_{0}^{16} : \frac{1}{4} [sin (u)]_{0}^{16}

= \frac{1}{4} [sin (u)]_{0}^{16}

带入上下限计算后得:

sin (16)

= \frac{1}{4} sin (16)

作图

流行的例子

integral from 1 to 4 of 1/(p^2+p-6)

integral from 1 to x of 8/(3t^3)

integral from 0 to 1 of 4x^3-2x+6

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

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