What is the integral of-4cos(2t) ?

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

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integral of-4cos(2t)

\int - 4 cos (2 t) d t

- 2 sin (2 t) + C

Solution steps

\int - 4 cos (2 t) d t

Take the constant out:

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

= - 4 \cdot \int cos (2 t) d t

Apply u-substitution

= - 4 \cdot \int cos (u) \frac{1}{2} d u

Take the constant out:

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

= - 4 \cdot \frac{1}{2} \cdot \int cos (u) d u

Use the common integral:

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

= - 4 \cdot \frac{1}{2} sin (u)

Substitute back

u = 2 t

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

Simplify

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

= - 2 sin (2 t)

Add a constant to the solution

= - 2 sin (2 t) + C