Area of the region bounded by $y=|x-1|$ and $y=1$ is

We have, $y = x - 1$ , if $x - 1 \ge 0$ $y = - x + 1$ , if $x - 1< 0$ Required area = area of shaded region $A=\int\limits_{0}^{2}1 dx-\left[\int\limits_{0}^{1}\left(1-x\right)dx+\int\limits_{1}^{2}\left(x-1\right)dx\right]$ $=\left[x\right]_{0}^{2}-\left[x-\frac{x^{2}}{2}\right]_{0}^{1}-\left[\frac{x^{2}}{2}-x\right]_{1}^{2}$ $=2-\frac{1}{2}-\frac{1}{2}=1$ s unit

Area of the region bounded by $y=|x-1|$ and $y=1$

Notes on applications of integrals

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

Area of the region bounded by $y=|x-1|$ and $y=1$ is

The Correct Option is B

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Notes on applications of integrals

Concepts Used:

Applications of Integrals