The area of the region bounded by the curve \( y=|x| \), \( x \)-axis and the lines \( x=-5 \) and \( x=5 \) is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 25 sq.units.
\( y=|x| \) is symmetric about the y-axis, so the area is twice the area from 0 to 5, where \( |x|=x \):
\( \displaystyle \text{Area}=\int_{-5}^{5}|x|\,dx \)
\( \displaystyle =2\int_{0}^{5}x\,dx \)
\( \displaystyle =2\left[\frac{x^2}{2}\right]_{0}^{5} \)
\( \displaystyle =2\times\frac{25}{2}=25 \)
The area is 25 sq. units.
Shortcut: The region is two right triangles, each with base 5 and height 5: area \( =2\times\frac{1}{2}\times 5\times 5=25 \).