Solve ∫ 2θdθ

$$\int 2 \theta d \theta$$

Evaluate

$$С+\theta ^{2}$$

Solution Steps

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

$$2\int \theta \mathrm{d}\theta$$

Since \int \theta ^{k}\mathrm{d}\theta =\frac{\theta ^{k+1}}{k+1} for k\neq -1, replace \int \theta \mathrm{d}\theta with \frac{\theta ^{2}}{2}. Multiply 2 times \frac{\theta ^{2}}{2}.

$$\theta ^{2}$$

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.

$$\theta ^{2}+С$$

Differentiate w.r.t. θ

$$2\theta$$