Application of Integrals

The area (in sq. units) of the region \(x, y) : 0 y 2|x| + 1, 0 y x2 + 1, |x| 3\ is

1. 323
2. 643
3. 173
4. 803

The area of the region bounded by the curves x(1 + y2) = 1 and y2 = 2x is:

1. 4 - 13
2. 2 - 13
3. 2 ( 2 - 13 )
4. 12 ( 2 - 13 )

The area of the region \(x,y):x2+4x+2 y |x+2| \ is equal to

1. 7
2. 24/5
3. 20/3
4. 5

The area of the region enclosed by the curves y=ex, y=|ex-1| and y-axis is :

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

If the area of the larger portion bounded between the curves x2+y2=25 and y=|x-1| is 14(b +c), b,c , then b+c is equal to

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