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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

Let J = ∫_ -1 ^2 ( ^ -1 (1)/(x) + ^ -1 x ) dx, K = ∫_ -2π ^ 7π (...

Let J=∫−12(cot⁡−11x+cot⁡−1x)dx,K=∫−2π7πsin⁡x∣sin⁡x∣dxJ = \int_{-1}^2 \left( \cot^{-1} \frac{1}{x} + \cot^{-1} x \right) dx, \quad K = \int_{-2\pi}^{7\pi} \frac{\sin x}{|\sin x|} dx. Then which of the following alternative(s) is/are correct ?

Options

  1. A2J+3K=8π2J + 3K = 8\pi
  2. B4J2+K2=26π24J^2 + K^2 = 26\pi^2
  3. C2J−K=3π2J - K = 3\pi
  4. DJK=25\frac{J}{K} = \frac{2}{5}

Correct answer

A. 2J+3K=8π2J + 3K = 8\pi

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