integral of cos((piy)/2)

解答

\int cos (\frac{π y}{2}) d y

\frac{2}{π} sin (\frac{π y}{2}) + C

求解步骤

\int cos (\frac{π y}{2}) d y

使用换元积分法

= \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 \int cos (u) d u

使用积分常见定则:

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

= \frac{2}{π} sin (u)

u = \frac{π y}{2}

代回

= \frac{2}{π} sin (\frac{π y}{2})

解答补常数

= \frac{2}{π} sin (\frac{π y}{2}) + C

\frac{d}{d x} (a sin (3 x) + b cos (3 x))

ma c l a u r in e^{- 4 x}

\int 5 - 4 x - x^{2} d x

\int_{0}^{a} a^{2} - x^{2} d x

\frac{\partial}{\partial x} (e^{2 x^{2}})