Solve ∫ 2acosθdθ

$$\int 2 a \cos \theta d \theta$$

Evaluate

$$2a\sin(\theta )+С$$

Solution Steps

Factor out the constant using \int af\left(\theta \right)\mathrm{d}\theta =a\int f\left(\theta \right)\mathrm{d}\theta .

$$2a\int \cos(\theta )\mathrm{d}\theta$$

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

$$2a\sin(\theta )$$

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

$$2a\sin(\theta )+С$$

Differentiate w.r.t. a

$$2\sin(\theta )$$