I need example in calculus

Step 1: Displacement is the definite integral of velocity.
$s = \int_{0}^{2} v(t) \, dt = \int_{0}^{2} 3t^{2} \, dt$ meters.

Step 2: Antiderivative formula.
$\int 3t^{2} \, dt = t^{3} + C$

Step 3: Evaluate definite integral.
$\left[ t^{3} \right]_{0}^{2} = (2)^{3} - (0)^{3} = 8 - 0 = 8$

The displacement is 8 meters.
8