I need example in calculus

March 16, 2026Mathematics

ScanSolve AI Answer

March 16, 2026

Answer

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

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Displacement is the definite integral of velocity. s = _0^2 v(t) \, dt = _0^2 3t^2 \, dt meters.

Asked on March 16, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on March 16, 2026

Step 1: Displacement is the definite integral of velocity. s = _0^2 v(t) \, dt = _0^2 3t^2 \, dt meters. Step 2: Antiderivative formula. 3t^2 \, dt = t^3 + C Step 3: Evaluate definite integral. [ t^3 ]_0^2 = (2)^3 - (0)^3 = 8 - 0 = 8 The displacement is 8 meters. 8