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Black Advanced Problems in Mathematics
Exam
Black Advanced Problems in Mathematics
Subject
Mathematics
Chapter
Indefinite and Definite Integration

Black Advanced Problems in Mathematics · Mathematics · Indefinite and Definite Integration

Value of _ h → 0 ∫_0^ π+h x^2 e^ -x^2 dx - ∫_0^π x^2 e^ -x^2 dx h...

Value of lim⁡h→0∫0π+hx2e−x2dx−∫0πx2e−x2dxh\lim_{h \to 0} \frac{\int_0^{\pi+h} x^2 e^{-x^2} dx - \int_0^\pi x^2 e^{-x^2} dx}{h} is equal to :

Options

  1. Aπ(1−π2)e−π2\pi(1 - \pi^2)e^{-\pi^2}
  2. B2π(1−π2)e−π22\pi(1 - \pi^2)e^{-\pi^2}
  3. Cπ(1−π)e−π\pi(1 - \pi)e^{-\pi}
  4. Dπ2e−π2\pi^2 e^{-\pi^2}

Correct answer

D. π2e−π2\pi^2 e^{-\pi^2}

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