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受欢迎的微积分 >

integral of-2/pi cos(pi/2 x)

解答

\int - \frac{2}{π} cos (\frac{π}{2} x) d x

解答

- \frac{4}{π ^{2}} sin (\frac{π x}{2}) + C

求解步骤

\int - \frac{2}{π} cos (\frac{π}{2} x) d x

提出常数:

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

= - \frac{2}{π} \cdot \int cos (\frac{π}{2} x) d x

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - \frac{2}{π} \cdot \int cos (\frac{π x}{2}) d x

使用换元积分法

= - \frac{2}{π} \cdot \int cos (u) \frac{2}{π} d u

提出常数:

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

= - \frac{2}{π} \cdot \frac{2}{π} \cdot \int cos (u) d u

使用积分常见定则:

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

= - \frac{2}{π} \cdot \frac{2}{π} sin (u)

u = \frac{π x}{2}

代回

= - \frac{2}{π} \cdot \frac{2}{π} sin (\frac{π x}{2})

化简

- \frac{2}{π} \cdot \frac{2}{π} sin (\frac{π x}{2}) : - \frac{4}{π ^{2}} sin (\frac{π x}{2})

= - \frac{4}{π ^{2}} sin (\frac{π x}{2})

解答补常数

= - \frac{4}{π ^{2}} sin (\frac{π x}{2}) + C

作图

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