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MCQMediumJEE Main 2023 · 29 January, Shift 1Definite Integrals

Mathematics Question from JEE Main 2023 · 29 January, Shift 1

Let f(x)=x+aπ2−4 sin⁡x+bπ2−4 cos⁡x,  x∈Rf(x) = x + \frac{a}{\pi^2 - 4}\,\sin x + \frac{b}{\pi^2 - 4}\,\cos x, \; x \in \mathbb{R} be a function which satisfies f(x)=x+∫0π/2sin⁡(x+y) f(y) dy.f(x) = x + \int_{0}^{\pi/2} \sin(x + y)\,f(y)\, dy. Then (a+b)(a+b) is equal to:

  • A

    −π(π+2)-\pi(\pi + 2)

  • B

    −2π(π+2)-2\pi(\pi + 2)

  • C

    −2π(π−2)-2\pi(\pi - 2)

  • D

    −π(π−2)-\pi(\pi - 2)

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