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受欢迎的微积分 >

integral of-sin(2x)

解答

\int - sin (2 x) d x

解答

\frac{1}{2} cos (2 x) + C

求解步骤

\int - sin (2 x) d x

提出常数:

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

= - \int sin (2 x) d x

使用换元积分法

= - \int sin (u) \frac{1}{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 sin (u) d u

使用积分常见定则:

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

= - \frac{1}{2} (- cos (u))

u = 2 x

代回

= - \frac{1}{2} (- cos (2 x))

化简

= \frac{1}{2} cos (2 x)

解答补常数

= \frac{1}{2} cos (2 x) + C

作图

流行的例子

integral of (4x)/(x+3)

\int \frac{4 x}{x + 3} d x

integral of sqrt(x(x+1))

\int x (x + 1) d x

integral from 1 to 100 of 1/(x^2)

\int_{1}^{100} \frac{1}{x ^{2}} d x

implicit (dy)/(dx),2x=y^4

im pl i c i t \frac{d y}{d x}, 2 x = y^{4}

limit as x approaches 0 of x/(-4x^3-8x)

x \to 0 lim (\frac{x}{- 4 x ^{3} - 8 x})