Area Under the Curve Questions - JEE

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:

The value of 'a' (a > 0) for which the area bounded by the curve $y = \frac{x-1}{6-x^2}$, $y = 0$, $x = a$ and $x = 2a$ has the least value, is

The region represented by |x − y| ≤ 2 and |x + y| ≤ 2 is bounded by a

The area (in sq. units) bounded by $y^2=x$ and $x^2=y$. [JEE Main 2019]

Given the region $\dfrac{y^2}{2} \le x \le y + 4$, find the area of the region (in square units).

Area of the region $\{(x,y)\,:\,y\ge0,\,y\le x,\,y\le 2-x\}$. [JEE Main 2023]

Area of $\{(x,y)\,:\,x^2\le y\le\sqrt{x}\}$. [JEE Main 2023]

If the area enclosed by the parabolas $P_1:2y=5x^2$ 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 ___.

Find the area enclosed between the curves $ x + 2y^2 = 0 $ and $ x + 3y^2 = 1 $.

The area enclosed by $y=\sin x+\cos x$ and $y=|\cos x-\sin x|$ over $[0,\pi/2]$ is: [MAU009]

The region bounded by the curves $y = 2^x$ and $y = |x + 1|$ has area equal to:

If the area enclosed between the curves y = kx² and x = ky², (k > 0), is 1 square unit. Then k is:

Given the region bounded by the curves $y = x^2$, $y = \dfrac{1}{x}$ and the lines $y = 0$ and $x = t$ $(t > 1)$. If the area bounded by these curves is 1, then $t$ equals:

Sketch the region bounded by the curves $y = \log_e x$ and $y = (\log_e x)^2$. Also find the area of the region.

The area bounded by $y = x^2 + 2$ and $y = 2|x| - \cos x$ is of the form $\frac{p}{q}$ where $p$ and $q$ are relatively prime. Find $p - q$.

The area of the region $\{(x,y)\,:\,x^2+y^2\le1\le x+y\}$. [JEE Main 2020]

The area enclosed by the closed curve C given by the differential equation $\dfrac{dy}{dx}+\dfrac{x+a}{y-2}=0$, $y(1)=0$ is $4\pi$. Let P and Q be the points of intersection of C and the y-axis. If normals at P and Q on C intersect x-axis at R and S respectively, then the length of RS is:

The area of the region consisting of all points $(x, y)$ so that $x^2 + y^2 \leq 1$ and $|x| + |y| \leq 1$ is

Let $\alpha$ be the area of the larger region bounded by the curve $y^2=8x$ and the lines $y=x$ and $x=2$, which lies in the first quadrant. Then the value of $3\alpha$ is equal to ___.

Let $A=\{(x,y)\in\mathbb{R}^2:y\geq0,\,2x\leq y\leq\sqrt{4-(x-1)^2}\}$ and $B=\{(x,y)\in\mathbb{R}\times\mathbb{R}:0\leq y\leq\min\{2x,\sqrt{4-(x-1)^2}\}\}$. Then the ratio of the area of A to the area of B is:

The area of the region $A=\left\{(x,y):|\cos x-\sin x|\leq y\leq\sin x,\,0\leq x\leq\dfrac{\pi}{2}\right\}$ is:

21. Let $A_k$ be the finite area bounded by the line $y = kx + k$ and the parabola $y = x^2$, where $k$ is a positive real number. The value of $\displaystyle\lim_{k \to \infty} \dfrac{A_k}{k^3}$ equals:

Let $A_1$ be the area of the region bounded by the curves $y = \sin x, y = \cos x$ and Y-axis in the first quadrant. Also, let $A_2$ be the area of the region bounded by the curves $y = \sin x, y = \cos x, x$-axis and $x = \frac{\pi}{2}$ in the first quadrant. Then, (JEE Main 2021)

The area (in sq. units) bounded between the parabola $y=x^2$ and the line $y=x$ is: [MAU007]

Area Under the Curve Questions (274)