TS EAMCET · Maths · Indefinite Integration
If \(\int \frac{2 \sin 2 x-3 \cos x}{2 \sin ^2 x-3 \sin x+4} d x=f(x)+c\) where \(c\) is the constant of integration, then \(f\left(\frac{\pi}{2}\right)-f(0)=\)
- A \(2 \log 2\)
- B 0
- C \(\log \left(\frac{3}{4}\right)\)
- D 1
Answer & Solution
Correct Answer
(C) \(\log \left(\frac{3}{4}\right)\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text {} \int \frac{2 \sin 2 x-3 \cos x}{2 \sin ^2 x-3 \sin x+4} d x=\int \frac{\cos x(4 \sin x-3)}{2 \sin ^2 x-3 \sin x+4} d x \\ & \text { Let } \sin x=t, \cos x d x=d t=\int \frac{(4 t-3)}{2 t^2-3 t+4} d t \\ & 2 t^2-3 t+4=u \Rightarrow(4 t-3) d t=d u \\ &…
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