JEE Mains · Maths · STD 12 - 7.1 indefinite integral
If \(\int \frac{1}{a^2 \sin ^2 x+b^2 \cos ^2 x} d x=\frac{1}{12} \tan ^{-1}(3 \tan x)+\) constant, then the maximum value of \(\operatorname{asin} \mathrm{x}+\mathrm{b} \cos \mathrm{x}\), is :
- A \(\sqrt{40}\)
- B \(\sqrt{39}\)
- C \(\sqrt{42}\)
- D \(\sqrt{41}\)
Answer & Solution
Correct Answer
(A) \(\sqrt{40}\)
Step-by-step Solution
Detailed explanation
\( \int \frac{\sec ^2 x d x}{a^2 \tan ^2 x+b^2} \) \( \text { let } \tan ^2=t \) \( \sec ^2 d x=d t \) \( \int \frac{d t}{a^2 t^2+b^2} \) \( \frac{1}{a^2} \int \frac{d t}{t^2+\left(\frac{b}{a}\right)^2} \)…
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