Question:
The area bounded by the curves $y =$ cos $x$ and $y=$ sin $x$ between the ordinates $x = 0$ and $x = \frac{3\pi}{2}$ is
The area bounded by the curves $y =$ cos $x$ and $y=$ sin $x$ between the ordinates $x = 0$ and $x = \frac{3\pi}{2}$ is
Updated On: Jul 5, 2022
- $4\sqrt{2}+2$
- $4\sqrt{2}-1$
- $4\sqrt{2}+1$
- $4\sqrt{2}-2$
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The Correct Option is D
Solution and Explanation
$\int\limits^{\frac{\pi}{4}}_{0}\left(cos \,x - sin\,x\right)dx +\int\limits^{\frac{5\pi }{4}}_{\frac{\pi}{4}} \left(sin \,x - cos\,x\right)dx +\int\limits^{\frac{3\pi }{4}}_{\frac{5\pi }{4}}\left(cos \,x - sin\,x\right) =4\sqrt{2}-2$
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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
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