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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Definite Integration

NDA 2013 · Mathematics · Definite Integration

What is ∫_0^2 (d x)/(x^2+4) equal to?

What is ∫02dxx2+4\int_0^2 \frac{d x}{x^2+4} equal to?

Options

  1. Aπ2\frac{\pi}{2}
  2. Bπ4\frac{\pi}{4}
  3. Cπ8\frac{\pi}{8}
  4. DNone of the above

Correct answer

C. π8\frac{\pi}{8}

Step-by-step solution

∫02dxx2+4=12\int_0^2 \frac{d x}{x^2+4}=\frac{1}{2}\left[\tan ^{-1} \frac{x}{2}\right]_0^2=\frac{1}{2}[π4−0]=π8\left[\frac{\pi}{4}-0\right]=\frac{\pi}{8}
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