Solve ∫ (from 0 to 1) of pir^2

$$\int _ { 0 } ^ { 1 } \pi r ^ { 2 }$$

Evaluate

$$\pi r^{2}$$

Solution Steps

Evaluate the indefinite integral first.

$$\int \pi r^{2}\mathrm{d}x$$

Find the integral of \pi r^{2} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\pi r^{2}x$$

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.

$$\pi r^{2}\times 1-\pi r^{2}\times 0$$

Simplify.

$$\pi r^{2}$$

Differentiate w.r.t. r

$$2\pi r$$