Solve ∫ (from 0 to 2) of pi3^2d3

$$\int _ { 0 } ^ { 2 } \pi 3 ^ { 2 } d 3$$

Evaluate

$$18\pi d_{3}$$

Solution Steps

Evaluate the indefinite integral first.

$$\int \pi \times 3^{2}d_{3}\mathrm{d}x$$

Find the integral of \pi \times 3^{2}d_{3} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\pi \times 3^{2}d_{3}x$$

Simplify.

$$9\pi d_{3}x$$

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.

$$9\pi d_{3}\times 2-9\pi d_{3}\times 0$$

Simplify.

$$18\pi d_{3}$$

Differentiate w.r.t. d_3

$$18\pi$$