Read the passage below and answer following questions

The current through a wire depends on time as i=i₀​ + 3 αt², where i₀ ​= 10 A and α = 0.5 ​A/sec².

What is the charge passing through the wire for that interval t = 0 to t = 2s ?

24 s

$Charge , dq = Idt = (I_0 + 3\alpha t^2)dt $

$\text{Integrating both sides,}$

$ q = I_0​t+\alpha t^3 = 24C$