List of top Mathematics Questions on Area of the region bounded

An ant is observed crawling on a sheet of paper along a straight line given by equation \( y = 2x - 4 \). Area of the surface covered by the ant bounded by y-axis, x-axis and \( x = 1 \) is :

The area of the shaded region of the circle given below is equal to :

If a girl takes twice as long to row a distance against the stream as to row the same distance in the direction of the stream, then the ratio of speed of the girl in still water to the speed of stream is:

The area bounded by the lines \( y = 1 + |x + 1| \), \( x = -3 \), \( x = 3 \) and \( y = 0 \) is

Area bounded by the curve $y=x^{3}$ and line $y=4x$ is:

Area of the region bounded by the curves $x=y^{2},\; y=-1,\; y=2$ and y-axis is:

Which of the following expressions will give the area of region bounded by the curve $y=x^2$ and line $y=16$?

The area of the region bounded by the lines $x + 2y = 12$, $x = 2$, $x = 6$, and the $x$-axis is:

The area of the region bounded by the lines \( \frac{x}{7\sqrt{3a}} + \frac{y}{b} = 4 \), \( x = 0 \), and \( y = 0 \) is:

Find the particular solution of the differential equation \( \left( x e^{\frac{y}{x}} + y \right) dx = x \, dy \), given that \( y = 1 \) when \( x = 1 \).

Find the particular solution of the differential equation \( \frac{dy}{dx} = y \cot 2x \), given that \( y\left(\frac{\pi}{4}\right) = 2 \).

Find \( \frac{dy}{dx} \), if \( y = (\cos x)^x + \cos^{-1}(\sqrt{x}) \) is given:

Find the principal value of \( \tan^{-1}(1) + \cos^{-1}\left(-\frac{1}{2}\right) + \sin^{-1}\left(-\frac{1}{\sqrt{2}}\right) \):

Express \( \tan^{-1} \left( \frac{\cos x}{1 - \sin x} \right) \), where \( -\frac{\pi}{2}<x<\frac{\pi}{2} \), in the simplest form.

Show that the function \( f(x) = \sin x + \cos x \) is strictly decreasing in the interval \( \left( \frac{\pi}{4}, \frac{5\pi}{4} \right) \).

The volume of a cube is increasing at the rate of \( 6 \, {cm}^3/{s} \). How fast is the surface area of the cube increasing, when the length of an edge is \( 8 \, {cm} \)?

If \[ \begin{bmatrix} a & c & 0 \\ b & d & 0 \\ 0 & 0 & 5 \end{bmatrix} \] is a scalar matrix, then the value of \( a + 2b + 3c + 4d \) is:

The function \( f(x) = kx - \sin x \) is strictly increasing for:

The function \( f(x) = |x| + |x - 2| \) is

Let \( \vec{a} \) be any vector such that \( |\vec{a}| = a \). The value of \( |\vec{a} \times \hat{i}|^2 + |\vec{a} \times \hat{j}|^2 + |\vec{a} \times \hat{k}|^2 \) is:

The area of the region bounded by the curve \(y=\sqrt{3x+10}\), x-axis and between the lines x = -3 and x = 2 is equal to :

The area of the region bounded by |x| + |y| = 1, x ≥ 0 y ≥ 0 is :