integral of -2cos(t) — step-by-step solution

Let's compute the integral:

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

For the math expression:

2 \cdot \cos (t)

, since (sin(a))' = a'*cos(a), we try differentiating

\sin (t)

Let's differentiate:

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

ⓘ The derivative of sin(x) is cos(x):

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

\cos (t)

\cos (t)

You observe that the computed derivative and the original math expression are the same, except for a coefficient. So the integral is:

ⓘ The derivative of

- 2 \cdot \sin (t)

- 2 \cdot \cos (t)

, so

- 2 \cdot \sin (t)

is an antiderivative of

- 2 \cdot \cos (t)

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

- 2 \cdot \sin (t)

- 2 \cdot \sin (t)

▶Indefinite integrals are defined up to an additive constant C, so this yields:

- 2 \cdot \sin (t) + C