List of top Mathematics Questions on Application of Integrals asked in CUET (UG)

Find the total area of the region bounded between the curve \( y = x^3 \), the x-axis, and the vertical lines \( x = -1 \) and \( x = 1 \).

Find the total area of the region bounded by the parabola \( y^2 = 4x \) and the straight line \( y = x \).

Find the total area of the bounded region enclosed between the parabola curve \( y^2 = 8x \) and its vertical latus rectum boundary line.

Find the area of the region enclosed by the ellipse given parametrically by the coordinates \( x = 2\sin\theta \) and \( y = 3\cos\theta \) where \( 0 \le \theta \le 2\pi \).

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

The area of region bounded by the curve \[ y^2=4ax \] and the straight line \[ x=2a,\qquad a>0 \] in the first quadrant is:

The area (in sq. units) of the region bounded by the parabola y2 = 4x and the line x = 1 is

The area (in sq. units) of the region bounded by the curve \( y = x^5 \), the x-axis and the ordinates x = -1 and x = 1 is equal to

The area (in sq. units) of the region bounded by the parabola y2 = 4x and the line x = 1 is

The area (in sq. units) of the region bounded by the curve \( y = x^5 \), the x-axis and the ordinates x = -1 and x = 1 is equal to

For \[ f(x) = \int \frac{e^x}{\sqrt{4 - e^{2x}}} \, dx, \] if the point $\left(0, \frac{\pi}{2}\right)$ satisfies $y = f(x)$, then the constant of integration of the given integral is:

The value of \[ \int_{-1}^{1} \tan^{-1} x \, dx \] is:

The integral of the function \( \frac{1}{9 - 4x^2} \) is:

The value of \(\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{dx}{1 + \tan^{18}x}\) is:

The value of \( I = \int_{0}^{1.5} \left\lfloor x^2 \right\rfloor dx \), where [ ] denotes the greatest integer function, is:

The area of the region bounded by the line $y=4$ and the curve $y=x^{2}$ is ________.