Solve ∫ (from 0 to 2 cos θ) of ( r -r)rdr

$$\int _ { 0 } ^ { 2 \cos \theta } ( r - r ) r d r$$

Evaluate

$$0$$

Solution Steps

Combine r and -r to get 0.

$$\int _{0}^{2\cos(\theta )}0r\mathrm{d}r$$

Anything times zero gives zero.

$$\int _{0}^{2\cos(\theta )}0\mathrm{d}r$$

Evaluate the indefinite integral first.

$$\int 0\mathrm{d}r$$

Find the integral of 0 using the table of common integrals rule \int a\mathrm{d}r=ar.

$$0$$

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.

$$0+0$$

Simplify.

$$0$$

Differentiate w.r.t. θ

$$0$$