AP EAMCET · Maths · Indefinite Integration
\(\int \frac{13 \cos 2 x-9 \sin 2 x}{3 \cos 2 x-4 \sin 2 x} d x=\)
- A \(3 x-\frac{1}{2} \log |3 \cos 2 x-4 \sin 2 x|+c\)
- B \(\frac{x}{2}-3 \log |3 \cos 2 x-4 \sin 2 x|+c\)
- C \(3 x+\frac{1}{2} \log |3 \cos 2 x-4 \sin 2 x|+c\)
- D \(x+\frac{3}{2} \log |3 \cos 2 x-4 \sin 2 x|+c\)
Answer & Solution
Correct Answer
(A) \(3 x-\frac{1}{2} \log |3 \cos 2 x-4 \sin 2 x|+c\)
Step-by-step Solution
Detailed explanation
\( \text{Let } N = 13 \cos 2x - 9 \sin 2x \text{ and } D = 3 \cos 2x - 4 \sin 2x \). \( D' = \frac{d}{dx}(3 \cos 2x - 4 \sin 2x) = -6 \sin 2x - 8 \cos 2x \). \( N = aD + bD' \implies 13 \cos 2x - 9 \sin 2x = a(3 \cos 2x - 4 \sin 2x) + b(-8 \cos 2x - 6 \sin 2x) \).…
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