Question

The area (in square units) bounded by the line \(y = x\), the X-axis and the lines \(x = -2\) and \(x = 4\) is...

• A. \(6\)
• B. \(\frac{15}{2}\)
• C. \(\frac{17}{2}\)
• D. \(10\)

Hint:

The region lies on both sides of the x-axis, so add the two triangles.

Answer 1

The Correct Option is D

Step 1: Integrate with modulus:
$\int_{-2}^{4}|x|\,dx = \left[-\frac{x^2}{2}\right]_{-2}^0 + \left[\frac{x^2}{2}\right]_0^4$.

Step 2: Evaluate:
$= (0 + 2) + (8 - 0) = 10$.

Final Answer:
The area is $10$ sq. units, option (D). \[ \boxed{10} \]