Question

The area of the region enclosed between the curve \( y = |x| \), x-axis, \( x = -2 \)} and \( x = 2 \) is:

• A. \( \frac{4}{3} \)
• B. 16
• C. \( \frac{8}{3} \)
• D. 8

Hint:

For symmetric curves, calculate the area for half the domain and then double it to find the total area.

Answer 1

The Correct Option is D

The function \( y = |x| \) exhibits symmetry with respect to the \( y \)-axis. Consequently, the area can be calculated for \( x \in [0, 2] \) and then doubled. The integral representing this area is: \[ \text{Area} = 2 \int_0^2 x \, dx = 2 \left[ \frac{x^2}{2} \right]_0^2 = 2 \times \frac{4}{2} = 8. \]