KCET · Maths · Definite Integration
\( \int_{-2}^{2}|x \cos \pi x| d x \) is equal to
- A \( \frac{8}{\pi} \)
- B \( \frac{4}{\pi} \)
- C \( \frac{2}{\pi} \)
- D \( \frac{1}{\pi} \)
Answer & Solution
Correct Answer
(A) \( \frac{8}{\pi} \)
Step-by-step Solution
Detailed explanation
\( \int_{-2}^{2}|x \cos \pi x| d x = 2 \int_{0}^{2}|x \cos \pi x| d x \) \( = 2 \left( \int_{0}^{1/2} x \cos \pi x d x - \int_{1/2}^{3/2} x \cos \pi x d x + \int_{3/2}^{2} x \cos \pi x d x \right) \)
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