What is the integral from 0 to 2 of sin((pit)/2) ?

The integral from 0 to 2 of sin((pit)/2) is 4/pi

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integral from 0 to 2 of sin((pit)/2)

\int_{0}^{2} sin (\frac{π t}{2}) d t

\frac{4}{π}

Decimal Notation

1.27323 \dots

Solution steps

\int_{0}^{2} sin (\frac{π t}{2}) d t

Apply u-substitution

: \int_{0}^{π} sin (u) \frac{2}{π} d u

= \int_{0}^{π} 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_{0}^{π} sin (u) d u

Use the common integral:

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

= \frac{2}{π} [- cos (u)]_{0}^{π}

Compute the boundaries:

2

= \frac{2}{π} \cdot 2

Simplify

= \frac{4}{π}

\int 18 t^{8} e^{- t^{9}} d t

\frac{\partial}{\partial z} (x y sin (\frac{π z}{3}))

\frac{\partial}{\partial x} (x e^{y} - 3 yz)

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

\frac{x ^{2}}{x + 2}

What is the integral from 0 to 2 of sin((pit)/2) ?
The integral from 0 to 2 of sin((pit)/2) is 4/pi