📝 Integration From The Viewpoint Of Differential Equations

Q1. A dragster travels with velocity \(v(t) = 3t^2 - 2t + 5\) (m/s) from \(t = 0\) to \(t = 4\) s. What is the distance traveled?

💡 Difficulty: easy | ✅ Correct: C

Q2. Given the differential equation \(\frac{dy}{dx} = y \sin x\) with \(y(0) = 2\), what is \(y(\pi)\)?

💡 Difficulty: medium | ✅ Correct: C

Q3. A population obeys \(\frac{dP}{dt} = kP(1 - P/1000)\). If \(P(0) = 200\) and \(P(5) = 400\), estimate \(k\).

💡 Difficulty: hard | ✅ Correct: B