Application of Integrals

The parabola y2 = 4x divides the area of the circle x2 + y2 = 5 in two parts. The area of the smaller part is equal to :

1. 23 + 5 -1 ( 2 5 )
2. 23 + 5 -1 ( 2 5 )
3. 13 + 5 -1 ( 2 5 )
4. 13 + 5 -1 ( 2 5 )

The area (in square units) of the region enclosed by the ellipse x2 + 3y2 = 18 in the first quadrant below the line y = x is

1. 3 + 1
2. 3
3. 3 - 34
4. 3 + 34

The area of the region in the first quadrant inside the circle x2 + y2 = 8 and outside the parabola y2 = 2x is equal to :

1. 2 - 13
2. - 13
3. - 23
4. 2 - 23

Let the area of the region enclosed by the curves y = 3x, 2y = 27 - 3x and y = 3x - x x be A. Then 10A is equal to

1. 172
2. 154
3. 162
4. 184

If the area of the region \(x, y) : ax2 y 1x, 1 x 2, 0 < a < 1 \ is ( e 2) - 17 then the value of 7a - 3 is equal to :

1. 1
2. 0
3. 2
4. -1

The area enclosed between the curves y = x|x| and y = x - |x| is :

1. 83
2. 23
3. 43
4. 1

One of the points of intersection of the curves y=1+3x-2x2 and y= 1x is ( 12, 2 ). Let the area of the region enclosed by these curves be 124(l 5+m)-n e(1+ 5), where l, m, n N. Then l+m+n is equal to

1. 30
2. 29
3. 31
4. 32

The area (in sq. units) of the region described by \(x, y) : y2 2x, and y 4x - 1 \ is

1. 932
2. 1112
3. 89
4. 1132

The area enclosed by the curves xy+4y=16 and x+y=6 is equal to :

1. 28-30 e2
2. 30-28 e2
3. 30-32 e2
4. 32-30 e2

The area of the region \(x, y): y2 4x, x<4, xy(x-1)(x-2)(x-3)(x-4)>0, x 3 \ is

1. 323
2. 163
3. 83
4. 643

The area of the region enclosed by the parabolas y=4x-x2 and 3y=(x-4)2 is equal to :

1. 329
2. 143
3. 4
4. 6

The area (in square units) of the region bounded by the parabola y2=4(x-2) and the line y=2x-8, is :

1. 7
2. 8
3. 9
4. 6