Question

The area bounded by \( y = |x| \), \( y = 0 \) and \( |x| = \frac{1}{2} \) will be:

• A. \( \frac{3}{4} \)
• B. \( \frac{5}{4} \)
• C. \( \frac{5}{4} \)
• D. None of these

Hint:

For areas involving absolute values, split the integral based on the points where the function changes its sign.

Answer 1

The Correct Option is C

Step 1: Set up the integral.
The area can be calculated by integrating \( |x| \) from \( -\frac{1}{2} \) to \( \frac{1}{2} \).
Step 2: Conclusion.
Thus, the area bounded by the given curves is \( \frac{5}{4} \).
Final Answer: \[ \boxed{\frac{5}{4}} \]