JEE Mains · Maths · STD 12 - 7.2 definite integral
The function \(\mathrm{f}(\mathrm{x})\), that satisfies the condition \(\mathrm{f}(\mathrm{x})=\mathrm{x}+\int_{0}^{\pi / 2} \sin \mathrm{x} \cdot \cos y \mathrm{f}(\mathrm{y}) \mathrm{dy}\), is :
- A \(x+\frac{2}{3}(\pi-2) \sin x\)
- B \(x+(\pi+2) \sin x\)
- C \(x+\frac{\pi}{2} \sin x\)
- D \(x+(\pi-2) \sin x\)
Answer & Solution
Correct Answer
(D) \(x+(\pi-2) \sin x\)
Step-by-step Solution
Detailed explanation
The function \(\mathrm{f}(\mathrm{x})\), that satisfies the condition \(\mathrm{f}(\mathrm{x})=\mathrm{x}+\int_{0}^{\pi / 2} \sin \mathrm{x} \cdot \cos y \mathrm{f}(\mathrm{y}) \mathrm{dy}\), is : (1) \(x+\frac{2}{3}(\pi-2) \sin x\) (2) \(x+(\pi+2) \sin x\) (3)…
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