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受欢迎的微积分 >

integral of (sin(ax))/a

解答

\int \frac{sin ( a x )}{a} d x

解答

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

求解步骤

\int \frac{sin ( a x )}{a} d x

提出常数:

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

= \frac{1}{a} \cdot \int sin (a x) d x

使用换元积分法

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

提出常数:

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

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

使用积分常见定则:

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

= \frac{1}{a} \cdot \frac{1}{a} (- cos (u))

u = a x

代回

= \frac{1}{a} \cdot \frac{1}{a} (- cos (a x))

化简

\frac{1}{a} \cdot \frac{1}{a} (- cos (a x)) : - \frac{1}{a ^{2}} cos (a x)

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

解答补常数

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

作图

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