By evaluating `int i^(2)Rdt`,show that when a capacitor is charged by connecting it to a battery through a resistor,the energy dissipated as heat equals the energy stored in the capacitor.

Explanation

To show that the energy dissipated as heat equals the energy stored in the capacitor when it is charged through a resistor, we will evaluate the integral \( \int I^2 R \, dt \).

### Step-by-Step Solution:

1. **Understanding the Circuit**:
- We have a capacitor being charged through a resistor \( R \) from a battery. The current \( I \) in the circuit can be expressed as:
\[
I(t) = I_0 e^{-\frac{t}{RC}}
...