List of top Mathematics Questions on Area between Two Curves

Let the area of the region enclosed by the curves $ y = 3x $, $ 2y = 27 - 3x $, and $ y = 3x - x\sqrt{x} $ be $ A $. Then $ 10A $ is equal to:

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

Let $A$ be the area of the region
$\left\{(x, y): y \geq x^2, y \geq(1-x)^2, y \leq 2 x(1-x)\right\}$.
Then $540 A$ is equal to ______.

It the area enclosed by the parabolas $P_1: 2 y=5 x^2$ and $P_2: x^2-y+6=0$ is equal to the area enclosed by $P_1$ and $y=\alpha x, \alpha>0$, then $\alpha^3$ is equal to____

If the area of the region bounded by the curves $y ^2-2 y=-x, x+y=0$ is $A$, then $8 A$ is equal to _________

The area bounded by the curve y = sin(x) between x = 0 to 2π is,

Let ω = z$\bar{z}$ + k₁z + k₂iz + λ(1+i), k₁ , k₂ ∈ $\mathbb{R}$. Let Re(ω) = 0 be the circle C of radius 1 in the first quadrant touching the line y =1 and the y-axis. If the curve Im (ω) = 0 intersects C at A and B, then 30 (AB)² is equal to _____

If the solution curve f(x, y) = 0 of the differential equation (1+log_e x) $\frac{dx}{dy} $- x log_e x = e^y , x > 0, passes through the points (1,0) and (α, 2) then α^a is equal to

The area of the region bounded by the line y = x +1, and the lines x = 3 and x = 5 is

In the interval (0, π/2), area lying between the curves y = tan x and y = cot x and the X-axis is

Let the area enclosed by the lines x+y=2, y=0, x=0 and the curve f(x) = min{x²+3/4, 1+[x]} where [x] denotes the greatest integer ≤x, be A. Then the value of 12 A is____.

Let the solution curve x = x (y), 0<y< π/2 of the differential equation (log_e (cos y))² cos y dx - (1 + 3x log_e(cos y))sin y dy = 0 satisfy x(π/3)=1/2log_e2. If x(π/6)= 1/log_em-log_en ,where m and n are coprime, then mn is equal to

The area bounded by the curves y = |x² – 1| and y = 1 is

Let a curve y = y(x) pass through the point (3, 3) and the area of the region under this curve, above the x-axis and between the abscissae 3 and
$x(>3)\ be\ (\frac{y}{x})^3$
. If this curve also passes through the point (α,6√10) in the first quadrant, then α is equal to _______.

The area of the region bounded by y² = 8x and y² = 16(3 – x) is equal to

If the area of the region $\{(x, y) : x^{2/3} + y^{2/3} \leq 1, x + y \geq 0, y \geq 0\}$ is A, then $\frac{(256 A)}{\pi} $is equal to_______.

The area of the region given by A={(x,y); $x^2$≤y≤min{x+2,4−3x}} is

The area (in sq. units) of the region enclosed between the parabola y² = 2x and the line x + y = 4 is _______.

Let $y = y(x)$ be the solution curve of the differential equation
$\frac{dy}{dx} + \frac{2x^2 + 11x + 13}{x^3 + 6x^2 + 11x + 6}y = (x+3)(x+1), \quad x > -1.$
which passes through the point $(0, 1)$. Then $y(1)$ is equal to

Consider a curve y = y(x) in the first quadrant as shown in the figure. Let the area A₁ is twice the area A₂. Then the normal to the curve perpendicular to the line 2x – 12y = 15 does NOT pass through the point.

Let
$A1 = {(x,y):|x| <= y^2,|x|+2y≤8} $
and
$A2 = {(x,y) : |x| +|y|≤k}. $
If 27(Area A₁) = 5(Area A₂), then k is equal to :

The area of the region enclosed by
$y≤4x^2, x2≤9y\ and\ y≤4,$
is equal to

The area of the smaller region enclosed by the curves y² = 8x + 4 and
x²+y²+4√3x-4=0
is equal to

The area of the region
$\left\{(x,y) : y² ≤ 8x, y ≥ \sqrt2x, x ≥ 1 \right\}$
is

The area bounded by the curve
$y=|x^2−9| $
and the line y = 3 is

List of top Mathematics Questions on Area between Two Curves

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