Inequalities

To solve the problem, we need to determine the range of values of that satisfy the inequality:

1. Evaluate the Definite Integral:
We evaluate the integral on the left-hand side:

2. Set Up the Inequality:
Now substitute into the inequality:

3. Multiply Through by 2 to Eliminate Denominators:

4. Rearrange the Inequality:

5. Solve the Quadratic Inequality:
Factor the quadratic:

This inequality is satisfied when:

6. Conclusion:
The correct range of values for is

Final Answer:
The correct option is (C) -3 ≤ a ≤ 4.