JEE Mains · Maths · STD 12 - 7.2 definite integral
The integral \(\int_0^{\frac{\pi}{4}} \frac{136 \sin x}{3 \sin x+5 \cos x} d x\) is equal to :
- A \(3 \pi-50 \log _e 2+20 \log _e 5\)
- B \(3 \pi-25 \log _e 2+10 \log _e 5\)
- C \(3 \pi-10 \log _e(2 \sqrt{2})+10 \log _e 5\)
- D \(3 \pi-30 \log _e 2+20 \log _e 5\)
Answer & Solution
Correct Answer
(A) \(3 \pi-50 \log _e 2+20 \log _e 5\)
Step-by-step Solution
Detailed explanation
\( \mathrm{I}=\int_0^{\pi / 4} \frac{136 \sin \mathrm{x}}{3 \sin \mathrm{x}+5 \cos \mathrm{x}} \mathrm{dx} \) \( 136 \sin \mathrm{x}=\mathrm{A}(3 \sin \mathrm{x}+5 \cos \mathrm{x})+\mathrm{B}(3 \cos \mathrm{x}-5 \sin \mathrm{x}) \)…
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