Application of Integrals

If the area of the region \(x, y) : 1 - 2x y 4 - x2, x 0, y 0\ is , , N, ( , ) = 1, then the value of ( + ) is:

1. 73
2. 85
3. 67
4. 91

Let the area of the bounded region \(x, y) : 0 9x y2, y 3x - 6 \ be A. Then 6A is equal to .

If the area of the region bounded by the curves y = 4 - x24 and y = x-42 is equal to , then 6 equals

1. 210
2. 250
3. 240
4. 220

If the area of the region \(x, y) : 1 + x2 y \x + 7, 11 - 3x\\ is A, then 3A is equal to :

1. 50
2. 46
3. 49
4. 47

If the area of the region \(x, y) : |x - 5| y 4 x\ is A, then 3A is equal to .

A line passing through the point A(-2, 0) touches the parabola P: y2 = x - 2 at the point B in the first quadrant. The area of the region bounded by the line AB, parabola P and the x-axis, is :

1. 3
2. 73
3. 83
4. 2

The area of the region bounded by the curve y = \|x|, x|x-2|\, the x-axis and the lines x = -2 and x = 4 is equal to

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

1. 5123
2. 20483
3. 512
4. 10243

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

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

1. 14
2. 18
3. 16
4. 12