The area of the region bounded by curves \( y=|x-4| \), x = 1, x = 5 and the \( x \)-axis is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 5 Sq. units
Since |x − 4| = 4 − x for x < 4 and x − 4 for x ≥ 4, the area splits at x = 4:
\( \displaystyle \int_1^5|x-4|\,dx=\int_1^4(4-x)\,dx+\int_4^5(x-4)\,dx \)
\( \displaystyle =\frac{9}{2}+\frac{1}{2} \)
\( =5\ \text{sq. units} \)
Shortcut: The graph forms two triangles: base 3 and height 3 (area 9/2), and base 1 and height 1 (area 1/2). Total 5.