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JEE Main 2023 · 29 Jan · Shift 1

JEE Main 2023 Mathematics question on Definite Integrals and Areas

Let f(x)=x+aπ2−4sin⁡x+bπ2−4cos⁡x, x∈Rf(x) = x + \dfrac{a}{\pi^2 - 4}\sin x + \dfrac{b}{\pi^2 - 4}\cos x,\ x \in \mathbb{R} be a function which satisfies f(x)=x+∫0π/2sin⁡(x+y) f(y) dyf(x) = x + \displaystyle\int_{0}^{\pi/2} \sin(x+y)\, f(y)\, dy. Then (a+b)(a+b) is equal to
  1. A.
    −2π(π+2)-2\pi(\pi+2)
  2. B.
    −π(π−2)-\pi(\pi-2)
  3. C.
    −2π(π−2)-2\pi(\pi-2)
  4. D.
    −π(π+2)-\pi(\pi+2)
Show answer

Correct option: A

[JEE Main 2023 · 29 Jan · Shift 1]

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