AP EAMCET · Maths · Indefinite Integration
If \(\int \frac{3 \cos x-2 \sin x}{4 \sin x+5 \cos x} d x=A \log\)
\(|5 \cos x+4 \sin x|+B x+c\), then \(A\) and \(B\) are
- A \(A=\frac{22}{41}\) and \(B=\frac{-7}{41}\)
- B \(A=\frac{-22}{41}\) and \(B=\frac{7}{41}\)
- C \(A=\frac{-22}{41}\) and \(B=\frac{-7}{41}\)
- D \(A=\frac{22}{41}\) and \(B=\frac{7}{41}\)
Answer & Solution
Correct Answer
(D) \(A=\frac{22}{41}\) and \(B=\frac{7}{41}\)
Step-by-step Solution
Detailed explanation
We have, \(\int \frac{3 \cos x-2 \sin x}{4 \sin x+5 \cos x} d x\) \(=A \log (5 \cos x+4 \sin x)+B x+c\) On differentiating both sides, we get \(\frac{3 \cos x-2 \sin x}{4 \sin x+5 \cos x}=\frac{A(-5 \sin x+4 \cos x)}{4 \sin x+5 \cos x}+B\)…
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