Solve ∫ (2cost-2)dt

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

Evaluate

$$2\sin(t)-2t+С$$

Solution Steps

Integrate the sum term by term.

$$\int 2\cos(t)\mathrm{d}t+\int -2\mathrm{d}t$$

Factor out the constant in each of the terms.

$$2\int \cos(t)\mathrm{d}t+\int -2\mathrm{d}t$$

Use \int \cos(t)\mathrm{d}t=\sin(t) from the table of common integrals to obtain the result.

$$2\sin(t)+\int -2\mathrm{d}t$$

Find the integral of -2 using the table of common integrals rule \int a\mathrm{d}t=at.

$$2\left(\sin(t)-t\right)$$

If F\left(t\right) is an antiderivative of f\left(t\right), then the set of all antiderivatives of f\left(t\right) is given by F\left(t\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.

$$2\sin(t)-2t+С$$

Differentiate w.r.t. t

$$2\left(\cos(t)-1\right)$$