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受欢迎的微积分 >

integral of-picos(pix)

解答

\int - π cos (π x) d x

解答

- sin (π x) + C

求解步骤

\int - π cos (π x) d x

提出常数:

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

= - π \cdot \int cos (π x) d x

使用换元积分法

= - π \cdot \int cos (u) \frac{1}{π} d u

提出常数:

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

= - π \frac{1}{π} \cdot \int cos (u) d u

使用积分常见定则:

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

= - π \frac{1}{π} sin (u)

u = π x

代回

= - π \frac{1}{π} sin (π x)

化简

- π \frac{1}{π} sin (π x) : - sin (π x)

= - sin (π x)

解答补常数

= - sin (π x) + C

作图

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