Application of Integrals

The area of the region enclosed between the circles x2 + y2 = 4 and x2 + (y - 2)2 = 4 is:

1. 23(4 - 3 3)
2. 43(2 - 3)
3. 43(2 - 3 3)
4. 23(2 - 3 3)

Let the line x = -1 divide the area of the region \(x, y) : 1 + x2 y 3 - x \ in the ratio m : n, (m, n) = 1. Then m + n is equal to

1. 27
2. 28
3. 25
4. 26

The area of the region A = \(x, y) : 4x2 + y2 8 and y2 4x\ is:

1. + 23
2. 2 + 2
3. + 4
4. 2 + 13

The area of the region, inside the ellipse x2 + 4y2 = 4 and outside the region bounded by the curves y = |x| - 1 and y = 1 - |x|, is :

1. 2 - 1
2. 3( - 1)
3. 2( - 1)
4. 2 - 12

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