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 ______.

Question

Let $A_1$ be the bounded area enclosed by the curves $y=x^2+2$, $x+y=8$ and $y$-axis that lies in the first quadrant. Let $A_2$ be the bounded area enclosed by the curves $y=x^2+2$, $y^2=x$, $x=2$ and $y$-axis that lies in the first quadrant. Then $A_1-A_2$ is equal to

Answer 1

The area of the region, denoted by A, is calculated as follows: $A = \int_{1/3}^{1/2} (2x^2 - 2x^3 - (1-x)^2) dx$ $ = \frac{1}{3} [2x^2 - x^3 - (1-x)^3]_{1/3}^{1/2}$ $ \therefore A = \frac{108}{5}$ $ \Rightarrow 540A = \frac{108}{5} \times 540$ $ = 25$ Therefore, the correct answer is 25.

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 ______.

Correct Answer: 25

Solution and Explanation

Top Questions on Area between Two Curves

Questions Asked in JEE Main exam

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 ______.

Correct Answer: 25

Solution and Explanation

Top Questions on Area between Two Curves

Questions Asked in JEE Main exam

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 ______.