Application of Integrals · Question 9

The area of the region R = \(x, y) : xy 8, 1 y x2, x 0\ is

1. 23(20 e(2) + 9)
2. 13(40 e(2) + 27)
3. 13(49 e(2) - 15)
4. 23(24 e(2) - 7)

Let P1 : y = 4x2 and P2 : y = x2 + 27 be two parabolas. If the area of the bounded region enclosed between P1 and P2 is six times the area of the bounded region enclosed between the line y = x, > 0 and P1, then is equal to :

1. 12
2. 15
3. 8
4. 6

Let A1 be the bounded area enclosed by the curves y = x2 + 2, x + y = 8 and y-axis that lies in the first quadrant. Let A2 be the bounded area enclosed by the curves y = x2 + 2, y2 = x, x = 2, and y-axis that lies in the first quadrant. Then A1 - A2 is equal to

1. 23(2 2 + 1)
2. 23(3 2 + 1)
3. 23( 2 + 1)
4. 23(4 2 + 1)

Let f( ) denote the area of the region in the first quadrant bounded by x = 0, x = 1, y2 = x and y = | x - 5| - |1 - x| + x2. Then (f(0) + f(1)) is equal to

1. 12
2. 14
3. 9
4. 7

Let the area of the region bounded by the curve y = \ x, x\, lines x = 0, x = 3 2, and the x-axis be A. Then, A + A2 is equal to .

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