What is the value of B ?
For the next two (02) items that follow : Let \( \int \frac{\sin \theta d\theta}{(2 + \cos \theta)(3 + 4\cos \theta)} = A \ln |2 + \cos \theta| + B \ln |3 + 4\cos \theta| \)
- A. -\frac{2}{5}
- B. -\frac{1}{5} ✓
- C. \frac{1}{5}
- D. \frac{2}{5}
Correct Answer: B. -\frac{1}{5}
Explanation
From the partial fraction decomposition in the previous question, the coefficient of \( \ln|4t+3| \) after integrating \( \frac{-4/5}{4t+3} \) is \( -1/5 \). Therefore, B = -1/5.
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