WBJEE · Maths · Definite Integration
Suppose \(M=\int_{0}^{\pi / 2} \frac{\cos x}{x+2} d x\) \(N=\int_{0}^{\pi / 4} \frac{\sin x \cos x}{(x+1)^{2}} d x\) Then, the value of \((M-N)\) equals
- A \(\frac{3}{\pi+2}\)
- B \(\frac{2}{\pi-4}\)
- C \(\frac{4}{\pi-2}\)
- D \(\frac{2}{\pi+4}\)
Answer & Solution
Correct Answer
(D) \(\frac{2}{\pi+4}\)
Step-by-step Solution
Detailed explanation
Given, \(M=\int_{0}^{\pi / 2} \frac{\cos x}{(x+2)} d x\) and \(\quad N=\int_{0}^{\sqrt{4}} \frac{\sin x \cos x}{(x+1)^{2}} d x\) \(\Rightarrow \quad N=\int_{0}^{\pi / 4} \frac{1}{2} \frac{\sin 2 x}{(x+1)^{2}} d x\) Put \(2 x=t \Rightarrow d x=\frac{d t}{2}\)…
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