MHT CET · Maths · Definite Integration
\(\int_0^2 \frac{3 x+1}{x^2+4} d x=\)
- A \(\log (2 \sqrt{2})+\frac{\pi}{4}\)
- B \(\log (2 \sqrt{2})+\frac{\pi}{6}\)
- C \(\log (2 \sqrt{2})+\frac{\pi}{8}\)
- D \(\log (2 \sqrt{2})+\frac{\pi}{12}\)
Answer & Solution
Correct Answer
(C) \(\log (2 \sqrt{2})+\frac{\pi}{8}\)
Step-by-step Solution
Detailed explanation
\( \int_0^2 \left(\frac{3x}{x^2+4} + \frac{1}{x^2+4}\right) dx \) \( = \left[ \frac{3}{2}\ln(x^2+4) + \frac{1}{2}\arctan\left(\frac{x}{2}\right) \right]_0^2 \)
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