Area Under the Curve Questions - JEE

The area bounded by the curve $y^2=4ax$ and its latus rectum is: [MAU006]

By drawing the graphs, find $f(x)$ as shown and evaluate \[\int_{-1}^{1} f(x)\, dx\] where $f(x)$ is the piecewise linear function forming triangles with peak value $1/2$ at $x = 0$, $x = \pm 1$ as shown in the graph.

The area of the region ABCD bounded by the curves y = x2, y = 2 − x2, and x = 1 (as shown in the figure) is equal to (in sq. units):

The area bounded by the curve $y^2 = 1 - x$ and the lines $y = \frac{lx}{x}$, $x = -1$ and $x = \frac{1}{e}$ is

Area of the region $y^2\le2x$ and $y\ge x-4$. [JEE Main 2020]

Area of region bounded by $y-x=2$, x-axis and $x=0,4$. [JEE Main 2020]

Area bounded by $y=x-x^2$ and the $x$-axis. [JEE Main 2019]

The area bounded by the curves $y=|x-1|+|x-2|$ and $y=3$ is equal to

The area enclosed between $y=x^3$ and $y=x$ is: [MAU018]

The area of the region bounded by the curves $y = |x - 2|$, $x = 1$, $x = 3$ and the $x$-axis is

If the area bounded by $y^2=4x$ and $y=4x-2$ is $A$, find $A$. [JEE Main 2021]

The area (in sq. units) bounded by the curves $y=\sqrt{x}$, $2y-x+3=0$, $x$-axis lying in the first quadrant is: [MAU001]

Area bounded by $y=e^x$, its tangent at $(0,1)$ and x-axis. [JEE Main 2022]

The value of the parameter 'a' such that the area bounded by $y = a[x^2] + ax + 1$, coordinate axes and the line $x = 1$ attains its least value, is equal to

The area of the region enclosed by the curve $f(x)=\max\{\sin x,\cos x\},\ -\pi\leq x\leq\pi$ and the $x$-axis is

Area of region $y=2\sin x$, $y=\cos2x$, $0\le x\le\pi/6$. [JEE Main 2021]

If $A=\dfrac{1}{2}\begin{bmatrix}1 & \sqrt{3}\\-\sqrt{3} & 1\end{bmatrix}$, then:

Area bounded by $y=\sin x$ and x-axis from $x=0$ to $x=2\pi$. [JEE Main 2023]

Let $\Delta$ be the area of the region $\{(x,y)\in\mathbb{R}^2:x^2+y^2\leq21,\,y^2\leq4x,\,x\geq1\}$. Then $\dfrac{1}{2}\!\left(\Delta-21\sin^{-1}\dfrac{2}{\sqrt{7}}\right)$ is equal to:

The area enclosed between the curve $y = \log_e(x + e)$ and the coordinate axes is

The area of the plane region bounded by the curves $x + 2y^2 = 0$ and $x + 3y^2 = 1$ is equal to

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

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

The area of the loop formed by the curve given by $x = a(1-t^2)$, $y = at(1-t^2)$, $-1 \leq t \leq 1$ is

Area Under the Curve Questions (274)