List of top Mathematics Questions on Curves

The area (in square units) of the region bounded by curves \( y = x \) and \( y = x^3 \) is:

For the curve \( y(1 + x^2) = 2 - x \), if \(\frac{dy}{dx} = \frac{1}{A}\) at the point where the curve crosses the x-axis, then the value of \( A \) is:

A particle moves along the curve \(6x = y^3 + 2\). The points on the curve at which the \(x\) coordinate is changing 8 times as fast as \(y\) coordinate are:

The area (in square units) bounded by the curve y = |x−2| between x = 0, y = 0, and x = 5 is:

The area (in square units) enclosed between the curve $x^2 = 4y$ and the line $x = y$ is:

The slope of normal to the curve \(y = 3x^2-6x\) at x = 0 is:

The area of region bounded by the curve y²=x, the y-axis and between y = 2 and y = 4 is

The area of the region bounded by the curve x²=4y and the straight line x = 4y - 2 is

If the curve ay + x² = 7 and x³ = y, cut orthogonally at (1, 1), then the value of a is -

The orthogonal trajectories of the family of curves y = \(ax^3\) is

The angle of intersection of the curves y=x³ and 6y=7-x² at (1,1) is