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MCQMediumJEE Main 2025 · 4 April, Shift 1Linear Differential Equations

Mathematics Question from JEE Main 2025 · 4 April, Shift 1

Let f:[0,∞)→Rf: [0, \infty) \to \mathbb{R} be a differentiable function such that f(x)=1−2x+∫0xex−tf(t) dtf(x) = 1 - 2x + \int_0^x e^{x-t} f(t) \, dt for all x∈[0,∞)x \in [0, \infty). Then the area of the region bounded by y=f(x)y = f(x) and the coordinate axes is](streamdown:incomplete-link)

  • A

    5\sqrt{5}

  • B

    12\frac{1}{2}

  • C

    2\sqrt{2}

  • D

    22

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