Solve ∫ -gsinθdθ

$$\int - g \sin \theta d \theta$$

Evaluate

$$g\cos(\theta )+С$$

Solution Steps

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

$$-g\int \sin(\theta )\mathrm{d}\theta$$

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

$$g\cos(\theta )$$

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.

$$g\cos(\theta )+С$$

Differentiate w.r.t. g

$$\cos(\theta )$$