CUET Mathematics: CalculusApplication of Integrals. Free, no login required.

The area enclosed between $y^2 = 4x$, $x = 1$ and $x = 4$ in first quadrant is :

Area of the region bounded by the curve $y = \cos x$ and $x-axis$ between $x = 0$ and $x = \pi$ is:

The area of the region bounded by the curves $x = at^2$ and $y = 2at$ between the lines parallel to $y-axis$ corresponding to $t = 1$ and $t = 2$ is equal to :

If the supply function for a commodity is $p = 3+x^3$. Then the producer's surplus, if 10 units of the goods are sold, is:

The area bounded by the curve $y^2 = 2x$, $y$-axis and the line $y=1$, is

The area (in square units) bounded by the curve $y = x^2|x|$, x-axis and the lines $x=-2$ and $x=2$, is

The area lying between the curves $x^2=4y$ and $x=2y$ is

The area (in sq. units) bounded between the curves $x=e^y$, $x=e$ and x-axis in the first quadrant is

The area of the region lying in the first quadrant and bounded by $y=8x^2, x=0, y=1$ and $y=4$ is:

The area bounded by the y-axis, $y=\cos x$ and $y=\sin x$, when $0\leq x\leq\frac{\pi}{4}$, is

The area bounded by an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and the lines $x=0, x=ae$ and the $x$-axis in the first quadrant, where $e$ is the eccentricity of the ellipse, is:

Area bounded by the curves $y=x^3$, $y=x+6$ and $x=0$ is

The area of the region bounded by the curve $y=\sqrt{9-x^2}$ and x-axis is

The area of the region bounded by the curve $x^2=4y$, the line $x=4y-2$ and x-axis is

The area of the region bounded by the curve $y=|x|$, x-axis and the lines $x=-5$ and $x=5$ is

The area (in sq.units) bounded by the lines $y=2x+3$, $y=0$ between $x=-2$ and $x=1$ is

If the area bounded by the parabola $x^2+my=0, m>0$ between its vertex and the latus rectum is $\dfrac{3}{2}$ square units, then the value of $m$ is

The area of the smaller region bounded by ellipse $\dfrac{x^2}{16}+\dfrac{y^2}{9}=1$ and the straight line $3x+4y=12$ is

The area (in sq. units) of the region bounded by $x^2=4y, y=1, y=9$ and $x=0$ in the first quadrant is :

The area of the region bounded by the line $3x - y + 2 = 0$, the $x-axis$ and the ordinates $x = -1$ and $x = 1$ is:

The area of the region $\{(x,y): x^2 \le y \le x\}$ is:

If the area(in square units) bounded by the curves $y^2 = 4x$ and $y = x$ is $\dfrac{k^3}{3}$, then the value of $k$ is:

If the supply curve is $p = \sqrt{9+x}$ and the quantity sold in market is 7 units, then the producer's surplus will be

The area bounded by the curve $y = \tan x$, $x = -\dfrac{\pi}{6}, x = \dfrac{\pi}{6}$ and $y=0$ is

The area (in square units) of the region bounded by the curve $x = y^3, y = -1, y = 2$ and $x = 0$ is:

The area (in sq. units) of the region in the first quadrant enclosed between the line $x + y = 2$, parabola $y^2 = x$ and the x-axis, is

The area (in sq. units) of the region bounded by the curve $x=at^2$, $y=2at$ between the ordinates corresponding to t = 1 and t = 2 is

The area (in sq. units) of the region bounded by the line $2y=3x+6$, x-axis and the ordinates x=-3 and x=1 is:

Area of the region bounded by the curve $y=\sin x, y=\cos x$ and $x-$axis, $\left(0\le x\le\frac{\pi}{2}\right)$ is;

Area bounded by the curves

$y=\begin{cases}x+2, & x\ge-1\\-x, & x<-1\end{cases}$, $x=-2, x=3$ and $y=0$ is: