Application of Integrals

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

Three points O(0,0), P (a,a2 ), Q (-b,b2 ), a>0, b>0, are on the parabola y=x2. Let S1 be the area of the region bounded by the line PQ and the parabola, and S2 be the area of the triangle OPQ. If the minimum value of S1S2 is mn, (m,n)=1, then m+n is equal to .

The sum of squares of all possible values of k, for which area of the region bounded by the parabolas 2y2=kx and ky2=2(y-x) is maximum, is equal to :

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

The area of the region enclosed by the parabola (y-2)2=x-1, the line x-2 y+4=0 and the positive coordinate axes is .

The area (in sq. units) of the part of the circle x2+y2=169 which is below the line 5x-y=13 is 2 - 652+ -1 ( 1213 ), where , are coprime numbers. Then + is equal to .

Let the area of the region \(x, y): 0 x 3, 0 y \x2+2, 2x+2 \ \ be A. Then 12 A is equal to .