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

The integral of (sin(2t))/2 is -1/4 cos(2t)+C

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integral of (sin(2t))/2

\int \frac{sin ( 2 t )}{2} d t

- \frac{1}{4} cos (2 t) + C

Solution steps

\int \frac{sin ( 2 t )}{2} d t

Take the constant out:

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

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

Apply u-substitution

: \int sin (u) \frac{1}{2} d u

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

Take the constant out:

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

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

Use the common integral:

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

= \frac{1}{2} \cdot \frac{1}{2} (- cos (u))

Substitute back

u = 2 t

= \frac{1}{2} \cdot \frac{1}{2} (- cos (2 t))

Simplify

\frac{1}{2} \cdot \frac{1}{2} (- cos (2 t)) : - \frac{1}{4} cos (2 t)

= - \frac{1}{4} cos (2 t)

Add a constant to the solution

= - \frac{1}{4} cos (2 t) + C

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What is the integral of (sin(2t))/2 ?
The integral of (sin(2t))/2 is -1/4 cos(2t)+C