Solve ∫ (from pi to 2 pi) of -cos(θ)dθ

$$\int_{ \pi }^{ 2 \pi } - \cos ( \theta ) d \theta$$

Evaluate

$$0$$

Solution Steps

Evaluate the indefinite integral first.

$$\int -\cos(\theta )\mathrm{d}\theta$$

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

$$-\int \cos(\theta )\mathrm{d}\theta$$

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

$$-\sin(\theta )$$

The definite integral is the antiderivative of the expression evaluated at the upper limit of integration minus the antiderivative evaluated at the lower limit of integration.

$$-\sin(2\pi )+\sin(\pi )$$

Simplify.

$$0$$