What is the integral of sin((pit)/2) ?

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

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integral of sin((pit)/2)

\int sin (\frac{π t}{2}) d t

- \frac{2}{π} cos (\frac{π t}{2}) + C

Solution steps

\int sin (\frac{π t}{2}) d t

Apply u-substitution

: \int sin (u) \frac{2}{π} d u

= \int sin (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 sin (u) d u

Use the common integral:

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

= \frac{2}{π} (- cos (u))

Substitute back

u = \frac{π t}{2}

= \frac{2}{π} (- cos (\frac{π t}{2}))

Simplify

= - \frac{2}{π} cos (\frac{π t}{2})

Add a constant to the solution

= - \frac{2}{π} cos (\frac{π t}{2}) + C

y^{^{''}} - \frac{2}{t ^{2}} y = 0, y (- 1) = - 1, y^{^{'}} (- 1) = - 4

\int \frac{2 x ^{2} + x + 1}{( x + 3 ) ( x - 1 ) ^{2}} d x

n = 1 \sum \infty 1 6^{n} x^{n} n!

\frac{d y}{d x} = 6 x - 30

\int x x^{2} + 7 d x

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