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受欢迎的微积分 >

integral of sin((npix)/1)

解答

\int sin (\frac{nπ x}{1}) d x

解答

- \frac{1}{πn} cos (πn x) + C

求解步骤

\int sin (\frac{nπ x}{1}) d x

化简

= \int sin (πn x) d x

使用换元积分法

= \int \frac{sin ( u )}{πn} d u

提出常数:

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

= \frac{1}{πn} \cdot \int sin (u) d u

使用积分常见定则:

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

= \frac{1}{πn} (- cos (u))

u = πn x

代回

= \frac{1}{πn} (- cos (πn x))

化简

= - \frac{1}{πn} cos (πn x)

解答补常数

= - \frac{1}{πn} cos (πn x) + C

作图

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