List of top Mathematics Questions on applications of integrals asked in MHT CET

Find the area of the region bounded by the curve \(y^2 = 4x\) and the line \(x = 3\).

The ratio of areas bounded by the curves \[ y=\cos x \] and \[ y=\cos 2x \] between \[ x=0,\qquad x=\frac{\pi}{3} \] and the \(x\)-axis is:

If the area enclosed between the circle \(x^2+y^2=25\) and the parabola \(y^2=16x\) is \(A\), then \(A=\ ?\)

The area bounded by the X-axis and the curve \[ y=x(x-2)(x+1) \] is:

The shaded region in the following figure represents a solution set of

The area (in sq. units) of the region bounded by the parabola $x = \frac{y^2}{2}$ and the line $x = y + 4$ is

Find area bounded by region, y=3x+1, y=4x+1 and x=3?

The area bounded by the parabola $y^2 = 4ax$ and its latus-rectum $x = a$ is

The area of the region included between the parabolas $y^2 = 8x$ and $x^2 = 8y$ is

The area bounded by the curve \(y = x^3\), the \(x\)-axis and the lines \(x = 1\) and \(x = 4\) is

If \( \sin(x + y) + \cos(x + y) = \sin \left[ \cos^{-1} \left( \frac{1}{3} \right) \right] \), then \[ \frac{dy}{dx} = \]

The perimeter of a triangle is \(10\) cm. If one of its sides is \(4\) cm, then the remaining sides of the triangle, when the area of the triangle is maximum, are

The area of the region bounded by the curve \( y = \log x \), x-axis and the lines \( x = 1 \), \( x = e \) is

The area of the region bounded by the lines $y = 2x + 1, y = 3x + 1$ and $x = 4$ is

The area bounded by the curves $y = (x - 1)^2$, $y = (x + 1)^2$ and $y = \frac{1}{4}$ is