UPSC NDA Math Model Paper 7

Region bounded by y = 2 |x| and y = 4
To find the area of the region enclosed by y = 2 |x| and y = 4,
we need to draw the graph.
First, we need to find the point of intersection.
Given that, y = 2 |x| and y = 4
put y = 4 in y = 2 |x|.
⇒ 4 = 2|x|
⇒ 2 = |x|
⇒ x = 2 or x = -2.
Point of intersection are (2, 4), (-2, 4) and (0,0) Graph of the equation is y = 2 |x| and y = 4 triangle with base 4 and height is 4.
Area of triangle =

1

2

× base × height.
Area of triangle =

1

2

×4×4
Area of triangle = 8.
Hence, the area of the region enclosed by y = 2 |x| and y = 4 is 8.