The current in conductor varies with time `t` as `I = 2 t + 3 t^(2)` where `I` is in ampere and `t` in seconds. Electric charge flowing through a section of the conductor during `t = 2 sec` to `t = 3 sec` is

Options

A. 10
B. 24
C. 33
D. 44

Explanation

To find the electric charge flowing through a section of the conductor during the time interval from \( t = 2 \) seconds to \( t = 3 \) seconds, we start with the given current function:

\[ I(t) = 2t + 3t^2 \]

### Step 1: Understand the relationship between charge, current, and time
The electric charge \( Q \) that flows through a conductor over a time interval can be calculated using the integral of the current over that time interval:

\[ Q = \int_{t_1}^{t_2} I(t) \, dt \]
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