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KCET · Maths · Definite Integration

\( \int_{-2}^{2}|x \cos \pi x| d x \) is equal to

  1. A \( \frac{8}{\pi} \)
  2. B \( \frac{4}{\pi} \)
  3. C \( \frac{2}{\pi} \)
  4. D \( \frac{1}{\pi} \)
Verified Solution

Answer & Solution

Correct Answer

(A) \( \frac{8}{\pi} \)

Step-by-step Solution

Detailed explanation

\( \int_{-2}^{2}|x \cos \pi x| d x = 2 \int_{0}^{2}|x \cos \pi x| d x \) \( = 2 \left( \int_{0}^{1/2} x \cos \pi x d x - \int_{1/2}^{3/2} x \cos \pi x d x + \int_{3/2}^{2} x \cos \pi x d x \right) \)