Solve ∫ (from 0 to pi) of 4n^2dt

$$\int _ { 0 } ^ { \pi } 4 n ^ { 2 } d t$$

Evaluate

$$4\pi n^{2}$$

Solution Steps

Evaluate the indefinite integral first.

$$\int 4n^{2}\mathrm{d}t$$

Find the integral of 4n^{2} using the table of common integrals rule \int a\mathrm{d}t=at.

$$4n^{2}t$$

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.

$$4n^{2}\pi -4n^{2}\times 0$$

Simplify.

$$4n^{2}\pi$$

Differentiate w.r.t. n

$$8\pi n$$