CAT 2020 Slot 3 QA Question 22: The area, in sq. units, enclosed by the lines $x = 2$, $y = |x - 2| + 4$, the X-axis and the Y-axis is equal to

Question

The area, in sq. units, enclosed by the lines $x = 2$, $y = |x - 2| + 4$, the X-axis and the Y-axis is equal to

Accepted Answer

The bounded region lies between $x = 0$ and $x = 2$.

For $0 \leq x \leq 2$, $y = |x - 2| + 4 = 2 - x + 4 = 6 – x$

So the region is a trapezium with vertical parallel sides of lengths 6 and 4, and horizontal width 2.

Area = $\dfrac{1}{2} 	imes (6 + 4) 	imes 2 = 10$

Answer: (2) 10

The area, in sq. units, enclosed by the lines x=2x = 2x=2, y=∣x−2∣+4y = |x - 2| + 4y=∣x−2∣+4, the X-axis and the Y-axis is equal to