Application of Integrals

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

Let the area enclosed between the curves |y|=1-x2 and x2+y2=1 be . If 9 = + ; , are integers, then the value of | - | equals:

1. 15
2. 18
3. 33
4. 27

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

1. 323
2. 643
3. 173
4. 803

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

1. 4 - 13
2. 2 - 13
3. 2 ( 2 - 13 )
4. 12 ( 2 - 13 )

The area of the region \(x,y):x2+4x+2 y |x+2| \ is equal to

1. 7
2. 24/5
3. 20/3
4. 5

The area of the region enclosed by the curves y=ex, y=|ex-1| and y-axis is :

1. 1+ e2
2. e2
3. 1- e2
4. 2 e2-1