The area (in sq units) of the region described by $A=\left\{(x, y): x^{2}+y^{2} \leq 1\right.$ and $\left.y^{2} \leq 1-x\right\}$ is:

Shaded area $=\frac{\pi(1)^{2}}{2}+2 \int\limits_{0}^{1} \sqrt{(1-x)} d x $ $=\frac{\pi}{2}+\left.\frac{2(1-x)^{3 / 2}}{3 / 2}(-1)\right|_{0} ^{1} $ $=\frac{\pi}{2}+\frac{4}{3}(0-(-1))$ $=\frac{\pi}{2}+\frac{4}{3}$

$ \frac{\pi}{2} + \frac{4}{3} $

The area (in sq units) of the region described by $A=\left\{(x, y): x^{2}+y^{2} \leq 1\right.$ and $\left.y^{2} \leq 1-x\right\}$ is:

$ \frac{\pi}{2} + \frac{4}{3} $

The area (in sq units) of the region described by A={(x,y):x2+y2=1 and y2=1-x} is:

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Concepts Used:

Applications of Integrals

There are distinct applications of integrals, out of which some are as follows:

In Maths

Integrals are used to find:

The center of mass (centroid) of an area having curved sides
The area between two curves and the area under a curve
The curve's average value

In Physics

Integrals are used to find:

Centre of gravity
Mass and momentum of inertia of vehicles, satellites, and a tower
The center of mass
The velocity and the trajectory of a satellite at the time of placing it in orbit
Thrust

The area (in sq units) of the region described by $A=\left\{(x, y): x^{2}+y^{2} \leq 1\right.$ and $\left.y^{2} \leq 1-x\right\}$ is:

The Correct Option is A

Solution and Explanation

Top Questions on applications of integrals

Questions Asked in JEE Main exam

Concepts Used:

Applications of Integrals