Application of Integrals · Question 26

JEE Main 2025 (Online) 3rd April Evening ShiftMCQMedium📈 Topic in 74% papers+4−1

The area of the region \(x, y) : |x - y| y 4 x\ is

Answer

(4) 10243

|x - y| y -y x - y y 0 x 2y

region: x2 y 4 x, x 0

Intersection of y = x2 and y = 4 x:

x2 = 4 x x = 8 x = 64 (or x = 0)

A = 064 (4 x - x2 ) dx

= [ 83x3/2 - x24 ]064

= 83(512) - 40964

= 40963 - 1024 = 10243

Answer: (4)

JEE Main 2025 (Online) 3rd April Evening Shift

If the area of the region \(x, y) : |4 - x2 | y x2, y 4, x 0 \ is ( 80 2 - ), , N, then + is equal to .

JEE Main 2025 (Online) 2nd April Morning Shift

Let the area of the region \(x, y) : 2y x2 + 3, y + |x| 3, y |x - 1|\ be A. Then 6A is equal to :

JEE Main 2025 (Online) 29th January Morning Shift

The area (in sq. units) of the region \(x, y) : 0 y 2|x| + 1, 0 y x2 + 1, |x| 3\ is

JEE Main 2025 (Online) 28th January Morning Shift

The area of the region bounded by the curves x(1 + y2) = 1 and y2 = 2x is:

JEE Main 2025 (Online) 28th January Evening Shift

All JEE Main Mathematics chapters