Solve ∫ (from 0 to 360) of rdθ

$$\int _ { 0 } ^ { 360 } r d \theta$$

Evaluate

$$360r$$

Solution Steps

Evaluate the indefinite integral first.

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

Find the integral of r using the table of common integrals rule \int a\mathrm{d}\theta =a\theta .

$$r\theta$$

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.

$$r\times 360-r\times 0$$

Simplify.

$$360r$$

Differentiate w.r.t. r

$$360$$