\( 1 \leftarrow \quad \) Use symmetry to evaluate the following integral.

To evaluate the integral using symmetry, we first need to identify the function and its properties. If the integral is over a symmetric interval about the origin, and the function is odd (meaning \( f(-x) = -f(x) \)), the integral evaluates to zero. If the function is even (meaning \( f(-x) = f(x) \)), you can simplify the computation by evaluating the integral from 0 to the upper limit and then doubling the result. Considering the general case \( \int_{-a}^{a} f(x) \, dx \), if \( f(x) \) is odd, you get \( \int_{-a}^{a} f(x) \, dx = 0 \). If \( f(x) \) is even, use \( \int_{0}^{a} f(x) \, dx \) and simply double that value for the complete integral. Now, keep an eye on potential mistakes! A common error is to misidentify whether the function is odd or even, which can lead to incorrect conclusions about the integral's value.