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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Definite Integration

NDA 2023 · Mathematics · Definite Integration

Paragraph: Let I_1=∫_0^π (x)/(1+ ^2 x) d x and I_2=∫_0^π (1)/(1+ ^2...

Paragraph: Let I1=∫0πx1+cos⁡2xdxI_1=\int_0^\pi \frac{x}{1+\cos ^2 x} d x and I2=∫0π11+sin⁡2xdxI_2=\int_0^\pi \frac{1}{1+\sin ^2 x} d x
Question: What is the value of I2I_2 ?

Options

  1. Aπ2\frac{\pi}{\sqrt{2}}
  2. Bπ22\frac{\pi}{2 \sqrt{2}}
  3. C3π22\frac{3 \pi}{2 \sqrt{2}}
  4. Dπ42\frac{\pi}{4 \sqrt{2}}

Correct answer

A. π2\frac{\pi}{\sqrt{2}}

Step-by-step solution

I2=2π22=π2I_2=\frac{2 \pi}{2 \sqrt{2}}=\frac{\pi}{\sqrt{2}}
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