List of top Mathematics Questions on Area between Two Curves asked in JEE Main

If the area of the region $\{ (x, y) : |x - 5| \leq y \leq 4\sqrt{x} \}$ is $A$, then $3A$ is equal to

The area of the region enclosed by the curves $ y = x^2 - 4x + 4 $ and $ y^2 = 16 - 8x $ is:

If the area of the region bounded by the curves $ y = 4 - \frac{x^2}{4} $ and $ y = \frac{x - 4}{2} $ is equal to $ \alpha $, then $ 6\alpha $ equals:

The area of the region enclosed by the curves $ y = x^2 - 4x + 4 $ and $ y^2 = 16 - 8x $ 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 ______.

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:

Let the area enclosed by the lines $ x + y = 2 $, $ y = 0 $, $ x = 0 $, and the curve $ f(x) = \min \left\{ x^2 + \frac{3}{4}, 1 + [x] \right\} $, where $ [x] $ denotes the greatest integer less than or equal to $ x $, be $ A $. Then the value of $ 12A $ is ____________.

Let the solution curve $ x = x(y) $, $ 0 < y \leq \frac{\pi}{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 \left( \frac{\pi}{3} \right) = \frac{1}{2 \log_e 2} $. If $ x \left( \frac{\pi}{6} \right) = \frac{1}{\log_e m - \log_e n} $, where $ m $ and $ n $ are co-prime integers, then $ mn $ 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

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 ____ .

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 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 curves y = |x² – 1| and y = 1 is

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

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

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 (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

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 :