Solve ∫ (from 0 to 3) of t^2

$$\int _ { 0 } ^ { 3 } t ^ { 2 }$$

Evaluate

$$3t^{2}$$

Solution Steps

Evaluate the indefinite integral first.

$$\int t^{2}\mathrm{d}x$$

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

$$t^{2}x$$

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.

$$t^{2}\times 3-t^{2}\times 0$$

Simplify.

$$3t^{2}$$

Differentiate w.r.t. t

$$6t$$