Application of Integrals

Let the area of the region enclosed by the curve y = \ x, x\ and the x axis between x = - to x = be A. Then A2 is equal to .

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 of the region enclosed by the parabolas y = x2 - 5x and y = 7x - x2 is .

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

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 .