Question:
The area under the curve $y = | cos\, x - sin \,x |, 0 \le x\le\frac{\pi}{2}$, and above x-axis is :
The area under the curve $y = | cos\, x - sin \,x |, 0 \le x\le\frac{\pi}{2}$, and above x-axis is :
Updated On: Jun 17, 2022
- $2\sqrt{2}$
- $2\sqrt{2}-2$
- $2\sqrt{2}+2$
- $0$
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The Correct Option is B
Solution and Explanation
$y = | cos\, x - sin\, x |$
Required area $\int\limits^{\pi/4}_{{0}}(cos\, x -sin \,x) \,dx$
$=2\left[sin\,x+cos\,x\right]^{\pi/4}_{0}=2\left[\frac{2}{\sqrt{2}}-1\right]$
$=\left(2\sqrt{2}-2\right)$ s units
Required area $\int\limits^{\pi/4}_{{0}}(cos\, x -sin \,x) \,dx$
$=2\left[sin\,x+cos\,x\right]^{\pi/4}_{0}=2\left[\frac{2}{\sqrt{2}}-1\right]$
$=\left(2\sqrt{2}-2\right)$ s units
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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