CUET Mathematics Calculus > Application of Integrals PYQs

The area (in sq. units) of the region bounded by $y = -1, y = 2, x = y^3$ and $x = 0$ is equal to

The area (in sq. units) of the region enclosed by the curve $9x^2 + 4y^2 = 36$ is

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

The area of the region bounded by the line $y = 2x$ and the x-axis between $x = -2$ and $x = 2$ is

Area of the region bounded by the curve $y = \sin x$ and x-axis between $x = \frac{\pi}{2}$ and $x = \frac{3\pi}{2}$ is

The area of the smaller region of the circle $x^2 + y^2 = 8$ cut off by the line $x = 2$ is

Area of the region bounded by $y = x^2$ and the line $y = 16$ is

The area (in sq.units) of the region bounded by the curve $y = \cos x$ between $x = -\frac{\pi}{2}, x = \frac{\pi}{2}$ and the x-axis is

The area (in sq.units) of the region bounded by the line $2y + x = 8$, the x-axis and the lines $x = 2$ and $x = 4$ is

The area bounded by the x-axis and the parabola $y = 3x-x^2$ is:

If under pure competition demand and supply functions are given by $p = \sqrt{10 - x}$ and $p = \frac{1}{2}(x-2)$ respectively, where $p$ is price per unit and $x$ is quantity, then the consumer surplus is:

The area of the region bounded by the parabola $y^2 = 8x$ and its latus rectum in the first quadrant, is

Area of the region bounded by the curve $y = \sqrt{x}$ and lines $x + y = 2$, $y = 0$ is

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

The area (in sq. units) of the region bounded by the parabola $y^2 = 8x$ and the line $x = 2$ is

The area (in sq. units) of the region in the first quadrant bounded by $y = 3\sqrt{1-x^2}$, $x \in [0,1]$ and the x-axis is equal to

The area of the region $\{(x, y): x^2 + y^2 \leq 1 \leq x + y\}$ is

Shown below is the graph of parabola $y^2=x$, the area (in sq. units) of the shaded region is: <img src="https://balti.afterboards.in/OwkXae9o8YL4aIn" width="400px"/>

The area (in Sq. units) of the region bounded by $y = -2$, $y = 2$, $x = y^3$ and $x = 0$ is equal to

The area of the region bounded by the curves $y = x^2 + 2$, $y = x$, $x = 0$ and $x = 2$ is

The area (in sq. units) of the bigger portion of region enclosed by the curves $4x^2 + 9y^2 = 36$ and $2x + 3y = 6$ is

The area of the region bounded by the parabola $y^2 = x$ and the straight line $2y = x$ is

The area (in sq.units) of the region enclosed by the curve $y = \cos x$, $\frac{-\pi}{2} \leq x \leq \frac{\pi}{2}$ and the x - axis is:

The area of the region bounded by the curves $y = x$ and $y = x^3$ is:

The marginal cost of production of x units of a commodity is $56 + \frac{3}{2}x$. It is known that fixed costs are Rs.115. Then the total cost of producing 50 units is:-

If the area above x-axis, bounded by the curves $y = 3^{\beta x}$, $x = 0$ and $x = 3$ is $\frac{26}{\log_e 3}$, then the value of $\beta$ is:

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

Area (in sq. units) of the region bounded by the curves $y = -1$, $y = 2$, $x = y^3$ and $x = 0$ is

The area (in sq. units) of the region bounded by the curve $x^2 = 250y$, $y = 0$ and $x = 50$ is

Area (in sq. units) of the region bounded by the curve $y^2 = 4x$, $y$-axis and the line $y = 3$ is

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

Area of the bounded region between the curve $y = |x - 2|$ and the line $y = 2$ is:

The area bounded by $y = 3x + 1$, $x = 0$, $y = 0$ and $x = a$ is 8 Sq.units. Then value of $a$ (where $a > 0$) is

Area (in sq. units) of the region bounded by the curve $y^2 = 4x$, y-axis and the line $y = 3$ is

The area (in sq. units) bounded by the curve $y = \cos x$ and x-axis between $x = 0$ and $x = \frac{3\pi}{2}$ is

The area (in sq. units) of the region bounded by the curve $y = \sqrt{16-x^2}$ and x-axis is

The nearest integral value of the shaded area shown below is: <img src="https://balti.afterboards.in/RpM45g4gxR34DDz" width="400px"/>

Area (in sq. units) of the region bounded by curves $y^2 = x$ and $x = 4$ is

The area (in square units) of the region enclosed between the lines $x + y = 2$, $x = 0$, $x = 3$ and $x$-axis is equal to

The area (in square units) bounded by the curve $y = \cos x$ between $x = 0$ and $x = 2\pi$ in first quadrant is equal to:

The area (in square units) of the region bounded by the curve $x^2 = y$ and the straight line $y = 4$ in the first quadrant is equal to

The demand function for a commodity is $p = 35 - 2x - x^2$, then the consumer's surplus at equilibrium price $p_0 = 20$ is

The area (in sq. units) bounded by the parabola $y^2 = 4ax$, its latus rectum and the $x$-axis in the first quadrant is:

Area of region bounded by the curves $x = y^3$, $x = 0$ between $y = -1$ and $y = 2$ is:

The area (in square units) of the region bounded by the curves $3y^2 = ax$, $y = a$, $a > 0$ and $y$-axis is:

The area of the region bounded by the curves $y = x^2 + 2$ and $x$-axis, between $x = 0$ and $x = 3$ in the first quadrant is:

The area of the region bounded by y² = 9x, x = 2, x = 4 and the x-axis in the first quadrant, is

The area enclosed between the graph of y = x³ and the lines x = 0, y = 1, y = 8 is

The area (sq.units) bounded by the curve y = sinx, π ≤ x ≤ 2π and the x-axis is

The area of the region enclosed between the parabola $y = \frac{3x^2}{4}$ and the line $3x - 2y = 12$ is,

The area bounded by the curve $y = \log x, y = 0$ and $x = e$, is

The area of the region bounded by $y = -1$, $y = 2$, $x = y^3$ and $x = 0$ is $\frac{m}{n}$ sq. units, where $\gcd(m, n) = 1$, then $m - n$ is equal to:

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

The area bounded by the curve $y = 4 + 3x - x^2$ and $x$-axis is equal to

The area (in sq. units) bounded by the parabola $y^2 = 16x$ and its latus rectum is

The area of the region (in square units) bounded by $x=1, x=2$ and the curve $y^2 = 4x$ in the first quadrant is

Consider the region bounded by the lines $y - 1 = x, x = -2, x = 3$ and $x$ - axis. Then (A) The area of the bounded region is given by $\int_{-2}^{3}(x + 1)dx$ (B) The numerical value of the area is $\frac{15}{2}$ sq. units (C) The numerical value of the area is 8 sq. units (D) The numerical value of the area is $\frac{17}{2}$ sq. units Choose the **correct** answer from the options given below:

Area of the region bounded by the curve $y^2 = 4x$, $y$-axis and the line $y = 3$ is equal to

The area (in sq. units) of the region bounded by the parabola $y^2 = 4x$ 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 $y = 2\sqrt{1 - x^2}$, $x \in [0, 1]$ and $x$-axis is equal to

The area (in sq. units) of the region bounded by the lines $y = 2x + 3$, the x – axis and the ordinates $x = -2$ and $x = 2$ is equal to

The area (in sq. units) of the region bounded by the curve $y = \sin x, -2\pi \leq x \leq 2\pi$ and $x - axis$ is equal to

The area (in sq. units) of the region $\{(x,y): 3x^2 \leq y \leq |x|\}$ is equal to

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

The area (in sq. units) of the region enclosed by the ellipse $16x^2 + 25y^2 = 400$ is

The area (in sq. units) of the region bounded by the line $y = x + 2$, $x = 0$, $x = 1$ and $y = 0$ is

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

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

The area of the region enclosed between the curves $4 x^{2}=y$ and $y=4$ is :

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

The area of the region $\{(x, y) : y \geq x^2 \text{ and } y \leq |x|\}$ is

The area enclosed by the ellipse $\frac{x^2}{16} + \frac{y^2}{9} = 1$ is given by :

Calculate the shaded area as given below : <img src="https://balti.afterboards.in/mD6m255LRScuQ6k" width="300px"/>

The area enclosed between the curve $x^2 + y^2 = 16$ and the coordinate axes in the first quadrant is :

The area enclosed between $y^2 = 4x$, $x = 1$, $x = 4$ 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 enclosed between the curve $y = x^2 + 2$ and x-axis between $x = 0$ and $x = 3$ is :

Which of the following regions will represent the shaded area in the given figure ?<img src="https://balti.afterboards.in/WldIj2j494JVyIl" width="400px"/>

Area of the region bounded by the curve $|x| + |y| = 1$ and x-axis is :

The area of the shaded portion <img src="https://balti.afterboards.in/0Orw0ReJYISKyt0" width="300px"/> is :

Area of the region bounded by $y = -1$, $y = 2$, $x = y^3$ and $x = 0$ is :

The area of the region bounded by the curve $x = y^2$ and the line $x = 4$ is equal to :

The area bounded by $x = \sqrt{9 - y^2}$, $x - y + 3 = 0$ and x-axis is :

The area bounded by the parabola $y^2 = 4ax$ and $x^2 = 4ay$ is :

The area (in square units) bounded by the curve $y^2 = 4x$ and the line $x=1$ is :

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

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

The line $y = x$, partition the area of the circle $(x-1)^2 + y^2 = 1$, into two segments. The area of the major segment is

The portion of the area enclosed by the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$, that lies in the first quadrant is

The area (in square units) of minor segment of the circle $x^2 + y^2 = 25$ cut off by the line $x = \frac{5}{2}$ is

The area enclosed by the curve $y^2 = 4ax$ and its latus-rectum is

The smaller of the areas enclosed by the circle $x^2 + y^2 = 4$ and the line $x + y = 2$ is

The smaller area enclosed by the curve $y = |x|$ and the circle $(x-a)^2 + y^2 = a^2$ is:

The line $y = mx$ ($m > 0$) partitions the area of the circle $x^2 + y^2 = a^2$ ($a > 0$) in the ratio:

The area bounded by the curve $x^2 = 4y$ and the line $x = 4y - 2$ is :

The area enclosed by the ellipse $\frac{x^2}{9^2} + \frac{y^2}{6^2} = 1$ is:

The area of the region bounded by the parabola $y^2 = 4ax$ and its latus rectum is:

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