Definite Integr...

The area of the plane region bounded by the curves x + 2y² = 0 and x + 3y² = 1, is equal to

The volume of the solid generated by revolving about the y-axis the figure bounded by the parabola y = x² and x = y² is

A frustum of sphere is made by cutting two parallel planes of any sphere. If radius of sphere is 5 cm and distance between the plane is 1 cm. Then will be the curved surface of frustum when the distance of first plane from the centre of sphere is 2 cm.

The area enclosed by the parabola y² = 4ax and the straight line y = 2ax , is

Area bounded by the curve x² = 4y and the straight line x = 4y – 2 is

If the area bounded by y = ax² and x = ay², a > 0, is 1,then a =

The parabolas y² = 4x and x² = 4y divide the square region bounded by the lines x = 4, y = 4 and the co-ordinate axes. If S₁, S₂, S₃ are respectively the areas of these parts numbered from top to bottom, then S₁ : S₂ : S₃ is