Question

.Which one of the following is true when ds/dt=3t^2/2s

A.s=3√6t-3t^2+C/2
B.s=√t^3+C
C.s=√t^3/2+C
D.s=√3t/2+C

Answer 1

1) Given: ds / dt = 3t^2 / 2s

2) Separate variables: 2s ds = 3t^2 dt

3) Integrate both sides:

∫ 2s ds = ∫ 3t^2 dt

s^2 + constant = t^3 + constant

=> s^2 = t^3 + constant

=> s = √ (t^3 + constant)

Answer: option B.