What is the integral of (sin(x/2)cos(x/2)) ?

The integral of (sin(x/2)cos(x/2)) is -1/2 cos(x)+C

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integral of (sin(x/2)cos(x/2))

\int (sin (\frac{x}{2}) cos (\frac{x}{2})) d x

- \frac{1}{2} cos (x) + C

Solution steps

\int sin (\frac{x}{2}) cos (\frac{x}{2}) d x

Rewrite using trig identities

= \int \frac{1}{2} sin (x) d x

Take the constant out:

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

= \frac{1}{2} \cdot \int sin (x) d x

Use the common integral:

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

= \frac{1}{2} (- cos (x))

Simplify

= - \frac{1}{2} cos (x)

Add a constant to the solution

= - \frac{1}{2} cos (x) + C

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What is the integral of (sin(x/2)cos(x/2)) ?
The integral of (sin(x/2)cos(x/2)) is -1/2 cos(x)+C