If `int_0^1e^-x^2dx=a ,` then find the value of `int_0^1x^2e^-x^2dx` in terms of `a` .

Explanation

To solve the problem, we need to find the value of the integral \( \int_0^1 x^2 e^{-x^2} \, dx \) in terms of \( a \), where \( a = \int_0^1 e^{-x^2} \, dx \).

### Step-by-Step Solution:

1. **Define the Integral**:
Let \( I = \int_0^1 x^2 e^{-x^2} \, dx \).

2. **Substitution**:
...