Test: Application of Integrals- 1 - JEE MCQ

For which of the following values of m , is the area of the region bounded by the curve y = x - x² and the line y = mx equal to 9/2 ?

The area of the region bounded by the parabola (y−2)² = x−1,the tangent to yhe parabola at the point (2 , 3) and the x – axis is equal to

The area of the loop between the curve y = a sin x and the x – axis and x = 0 , x = π. is

The area bounded by the curve y² = x,line y = 4 and y – axis is equal to

The area enclosed by the curve xy² = a²(a − x) and the y – axis is

The area bounded by the curve y = x[x], the x – axis and the ordinates x = 1 and x = -1 is given by

The area bounded by the curves y = cos x and y = sin x between the ordinates x = 0 and x = π/2 is equal to

The area enclosed between the curves y = x³ ,x- axis and two ordinates x = 1 to x = 2 is [in square units]

The area bounded by y = log x , the x – axis and the ordinates x = 1 and x = 2 is

The area bounded by the curves y² = x³ and |y| = 2x is given by

The area bounded by the curve y = 2x - x² and the line x + y = 0 is

The area bounded by the parabola y = x² and the line y = x is

Area of the region bounded by the curves y = e^x, x = a , x = b and the x- axis is given by

The area bounded by the curves y² = 4x and y = x is equal to

The area bounded by the curves y = √x, 2y+3 = x and the x- axis in the first quadrant is

Let y be the function which passes through (1 , 2) having slope (2x + 1) . The area bounded between the curve and the x – axis is

AOB is the positive quadrant of the ellipse  in which OA = a and OB = b . The area between the arc AB and chord AB of the ellipse is

The area common to the circle x²+y² = 16 and the parabola y² = 6x is

The area included between the curves   is equal to

The area bounded by the curves y² = 20x and x² = 16y is equal to

The area bounded by the curves 

The area of the region bounded by the curves y = |x−2|, x = 1 , x = 3 and the x – axis is