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The value of the integral

 is:

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NIELIT Scientific Assistant ECE 5 Dec 2021 Official Paper
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  1. π 
  2. π/3
  3. π/5
  4. π/7

Answer (Detailed Solution Below)

Option 3 : π/5
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Detailed Solution

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Concept:

The given integral is:

This represents a double integral over the upper half of the unit circle centered at the origin. So, converting it into polar coordinates simplifies the integration process.

Let and

The region of integration becomes a semicircle:

Calculation:

In polar coordinates,

So, the integral becomes:

Correct Option:

The correct answer is: 3) π/5

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