What is the integral of cos((piy)/2) ?

The integral of cos((piy)/2) is 2/pi sin((piy)/2)+C

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integral of cos((piy)/2)

\int cos (\frac{π y}{2}) d y

\frac{2}{π} sin (\frac{π y}{2}) + C

Solution steps

\int cos (\frac{π y}{2}) d y

Apply u-substitution

: \int cos (u) \frac{2}{π} d u

= \int cos (u) \frac{2}{π} d u

Take the constant out:

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

= \frac{2}{π} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{2}{π} sin (u)

Substitute back

u = \frac{π y}{2}

= \frac{2}{π} sin (\frac{π y}{2})

Add a constant to the solution

= \frac{2}{π} sin (\frac{π y}{2}) + C

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

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}})

What is the integral of cos((piy)/2) ?
The integral of cos((piy)/2) is 2/pi sin((piy)/2)+C