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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

If ∫_0^π (x^3 ^4 x ^2 x)/(π^2 - 3π x + 3x^2) dx = λ ∫_0^ π/2 ^2 x...

If ∫0πx3cos⁡4xsin⁡2xπ2−3πx+3x2dx=λ∫0π/2sin⁡2xdx\int_0^\pi \frac{x^3 \cos^4 x \sin^2 x}{\pi^2 - 3\pi x + 3x^2} dx = \lambda \int_0^{\pi/2} \sin^2 x dx, then the value of λ\lambda is :

Options

  1. Aπ12\frac{\pi}{12}
  2. Bπ8\frac{\pi}{8}
  3. Cπ4\frac{\pi}{4}
  4. Dπ3\frac{\pi}{3}

Correct answer

A. π12\frac{\pi}{12}

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