Application of Integrals

If the area of the region \(x,y):-1 x 1, 0 y a+e|x|-e-x, a>0 \ is e2+8e+1e, then the value of a is :

1. 7
2. 5
3. 6
4. 8

The area of the region, inside the circle (x-2 3)2+y2=12 and outside the parabola y2=2 3 x is :

1. 3 -8
2. 6 -8
3. 3 +8
4. 6 -16

Let f:R be a twice differentiable function such that f(x+y)=f(x)f(y) for all x,y . If f'(0)=4a and f satisfies f''(x)-3af'(x)-f(x)=0, a>0, then the area of the region R=\(x,y) 0 y f(ax), 0 x 2\ is :

1. e2-1
2. e4+1
3. e2+1
4. e4-1

Let the function, f(x)= cases-3ax2-2, & x<1\ a2+bx, & x 1 cases be differentiable for all x , where a>1, b . If the area of the region enclosed by y=f(x) and the line y=-20 is + 3, , Z, then the value of + is .

The area of the region enclosed by the curves y=x2-4x+4 and y2=16-8x is :

1. 83
2. 5
3. 8
4. 43

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

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