JEE Mains · Maths · STD 12 - 7.2 definite integral
Let \(\quad f(x)=x+\frac{a}{\pi^2-4} \sin x+\frac{b}{\pi^2-4} \cos x\) \(x \in R\) be a function which satisfies \(f(x)=x+\int \limits_0^{\pi / 2} \sin (x+y) f(y) d y\). Then \(( a + b )\) is equal to \(............\)
- A \(-\pi(\pi+2)\)
- B \(-2 \pi(\pi+2)\)
- C \(-2 \pi(\pi-2)\)
- D \(-\pi(\pi-2)\)
Answer & Solution
Correct Answer
(B) \(-2 \pi(\pi+2)\)
Step-by-step Solution
Detailed explanation
\(f(x)=x+\int \limits_0^{\pi / 2}(\sin x \cos y+\cos x \sin y) f(y) d y\) \(f(x)=x+\int \limits_0^{\pi / 2}((\cos y f(y) d y) \sin x+(\sin y f(y) d y) \cos x).......(1)\) On comparing with \(f(x)=x+\frac{a}{\pi^2-4} \sin x+\frac{b}{\pi^2-4} \cos x, x \in R\) then…
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